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					                                                21e08496-211b-42ae-9c8c-585ac63e0204.xlsx


                      A                  B                 C                   D            E      F      G     H      I      J
 1   Basic Descriptive Statistics                                                                                     5▼
 2                                                                                                                   Score   Raw
 3                                                  Symbolic Formula         Function   Computed  Excel             Number Scores
 4                                 Name Symbol       See notes below          Name       Formula Function              i      X
 5                                  Sum     SX       X1 + X2 + X3 . . . + Xn   SUM                        ◄1               1     5
 6            Sample or Population Size   n or N                  n or N =   COUNT                        ◄2                     6
 7                  Degrees of Freedom      d.f.                     n-1=                                 ◄3                     7
 8          Sample or Population Mean       or m   sum/number = SX/n = AVERAGE                            ◄4                     5
 9                       Sum of Squares     SS                  S(X - ) = SUM, DEVSQ
                                                                          2
                                                                                                          ◄9                     3
                                              2
10                      Sample Variance     S                    SS/d.f. =    VAR.S                       ◄10                    8
11           Sample Standard Deviation       S               (SS / d.f.) = STDEV.S                       ◄11                    7
12              Intermediate Calculation                                 S/                               ◄12                    2
13       Sample Coefficient of Variation   Cvar                (S / )*100                                 ◄13                    1
14                 Legend                                                                                                        5
15   Labels                                      Check Data &                         9
16   Given Data                                  Sample Worksheet 1                   8
17   Order of Computation                        Quiz Data                            7
18   Cells using formulas                                                             6
19   Cells using function                                                             5
20   Cells using functions in a formula                                               6
21   Optional Data                                                                    7
22                                                                                    8
23                                                                                    9
24                                                                                    9
25                                                                                    5
26                                                                                    6
27
28                                                       Last Z score =            -0.72
29                                                              CVAR =             21.25
30
31                                             Worksheet Quiz 1 Data                 22
32                                             Enter this data in                    25
33                                              Column J                             13
34                                             and Complete                           9


                                                 Prepared by G. Lee Griffith, Ph.D. 9/13/2012
             21e08496-211b-42ae-9c8c-585ac63e0204.xlsx


     A   B             C                    D            E   F   G   H   I   J
35           Worksheet Quiz 1                     8
36                                               14
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              Prepared by G. Lee Griffith, Ph.D. 9/13/2012
             21e08496-211b-42ae-9c8c-585ac63e0204.xlsx


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              Prepared by G. Lee Griffith, Ph.D. 9/13/2012
                                          21e08496-211b-42ae-9c8c-585ac63e0204.xlsx


     K    L        M      N    O      P
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 2     DeviationSquared Std z-score
 3 Mean Score Dev Sc Dev      Z=
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                                           Prepared by G. Lee Griffith, Ph.D. 9/13/2012
                             21e08496-211b-42ae-9c8c-585ac63e0204.xlsx


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                              Prepared by G. Lee Griffith, Ph.D. 9/13/2012
                             21e08496-211b-42ae-9c8c-585ac63e0204.xlsx


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                              Prepared by G. Lee Griffith, Ph.D. 9/13/2012
Worksheet 2 Histogram

          Build Worksheet 2 Data: Use this data to construct a histogram

          Construct a histogram showing the number of each color of ribbon awarded at the state fair.
                               Ribbons Awarded at State Fair
                               Color of Ribbon                Frequency of Ribbon
                               White                                                 8
                               Red                                                   6
                               Blue                                                  1
                               Purple                                                4
                               Grand                                                 2
          Source: simulated

          Check Data: use this data to check your understanding of creating a histogram and in Sample Worksheet 2 quiz

          Construct a histogram showing the number of male drinkers in each category
          CLASSIFICATIONS OF PARTICIPANTS BY DRINKING CATEGORY
                               Q-F-V Category                 Number of Participants
                               Light                                                33
                               Moderate                                             54
                               Heavy                                                81
          Source: http://www.mass.gov/mdaa/mvcrimes/Psychophysical%20tests%20for%20DWI.pdf

          Worksheet Quiz 2 Data

          Construct a histogram for the data below and answer the questions in Worksheet 2 Quiz
                               College Student Alcohol Use in 1999
                               Category                         Percent (n = 13,819)
                                      Abstainer (past y)                             19.2
                                      Nonbinge drinker†                              36.6
                                      Occasional binge drinker‡                      21.4
                                    Frequent binge drinker§                          22.7
          †Students who consumed alcohol in the past year but did not binge.
          ‡Students who binged one or two times in a 2-week period.
          §Students who binged three or more times in a 2-week period.
the state fair.




and in Sample Worksheet 2 quiz




%20DWI.pdf
Worksheet 2 Pareto and Pie Chart

          Build Worksheet 2 Pareto and Pie Chart Data

          Construct two graphs. First a Pareto Chart. Be sure to sort the columns in the table by descending frequency
          Second construct a Pie Chart
          Madison County Indiana 1995 Frequency of Crimes Reported
                                          Crime                         Frequency
                                          ARSONS                                        8
                                          BURGLARIES                                   91
                                          MOTOR VEHICLE THEFTS                         46
                                          RAPES                                         6
                                          ROBBERIES                                     5
          Source: http://fisher.lib.Virginia.EDU/cgi-local/crimebin/new2.cgi




          Check Data and Sample Worksheet Quiz 2 Data:
          use the following data to check that you know how to create Pareto and Pie charts and to answer the sample Works
                                       Problem                                %
                                       Wrong Size                                    24
                                       Did not want                                  34
                                       Item was defective                            38
                                       No reason given                                 4
          This is simulated data on types of problems in goods returned to Target use it to construct a Pareto Diagram (sorted


          Worksheet Quiz 2 Data
          For the data below create a Pareto and Pie charts and answer the questions in Worksheet Quiz 2

          Table 1: Differences in Average Income and Family Size Among Families with Children, by Marital Status and Sex o
                                      Type of Family                 Mean Income          Median Income


                                      Married Couple Families                   $79,048               $62,931
                                      Male Householder, No Wife                  44,270                32,516
                                      Present
                                      Female Householder, No                     29,075                21,529
                                      Husband Present
          http://www.aspe.hhs.gov/hsp/marriage-well-being03/LitReview.pdf
escending frequency




o answer the sample Worksheet 2 quiz




ct a Pareto Diagram (sorted) and a pie chart.




by Marital Status and Sex of Household Head: 2000
             Income
             per
             Person
               $18,515
                 14,719

                  9,023
  Madison County Indiana 1995
  Frequency of Crimes Reported




Percentage of Various Types of Retu
ounty Indiana 1995
of Crimes Reported

              ARSONS
              BURGLARIES
              MOTOR VEHICLE THEFTS
              RAPES
              ROBBERIES




 Various Types of Returns


                       Wrong Size
                       Did not want
                       Item was defective
                       No reason given
Worksheet 2 Bar Graph
          Build Worksheet 2 Data: Use this data to build two bar graphs and compare with key

           Construct 2 graphs. The first to show which country has the lowest higher education rate.
           The second graph should show which country has the most gender difference in higher education rate.
           Percentage of the population in large industrialized countries who had completed education.
                                            Country                        Total      Male      Female
                                            Canada                            16.9         18        18.9
                                            France                             9.2       11.9        11.3
                                            Germany                           12.6       12.7          11
                                            Italy                              7.5        7.7         8.1
                                            Japan                             13.3       34.2        11.5
                                            United Kingdom                    11.7       15.7        11.7
                                            United States                     24.4       23.4        23.5
           Percentage of the population in large industrialized countries who had completed higher education, by age, sex, and
           source: http://nces.ed.gov/pubs/ce/c9723a01.html

           Check Data and Sample Worksheet Quiz Data: use this data to check your work and answer questions in Sample W
           Using the following data construct an absolute frequency bar graph and take the Sample Worksheet 2 Quiz.
           This data represents the marital status of Residents of Madison County Indiana who are 15 years and over.
                                           Group                       Frequency Percent
                                          Never married                    22,623         21.2

                                          Now married, except separated    61,567         57.6
                                          Separated                         1,392          1.3
                                          Widowed                           7,874          7.4
                                          Divorced                         13,481         12.6
           Source: http://factfinder.census.gov/servlet/QTTable?_bm=y&-qr_name=DEC_2000_SF3_U_DP2&-ds_name=DEC

           Worksheet Quiz 2 Data
           Construct a Bar Graph comparing household income in Madison and Marion Counties (Indiana) then take Workshe
                                                     Family Income        Madison      Marion
                                          Less than $10,000                   7.9          8.5
                                          $10,000 to $14,999                  7.2          6.2
                                          $15,000 to $24,999                 15.4         13.9
                                          $25,000 to $34,999                 14.3         14.2
                                          $35,000 to $49,999                   18         17.7
                                          $50,000 to $74,999                 19.7          20
                                          $75,000 to $99,999                  9.9          9.6
                                          $100,000 to $149,999                5.5          6.6
                                          $150,000 to $199,999                  1          1.6
                                          $200,000 or more                    1.1          1.7


           source 1: http://factfinder.census.gov/servlet/QTTable?_bm=y&-qr_name=DEC_2000_SF3_U_DP3&-ds_name=DE
           source 2: http://factfinder.census.gov/servlet/QTTable?_bm=y&-qr_name=DEC_2000_SF3_U_DP3&-ds_name=DE
 gher education rate.




higher education, by age, sex, and country: 1994


 nd answer questions in Sample Worksheet 2
 ample Worksheet 2 Quiz.
ho are 15 years and over.




00_SF3_U_DP2&-ds_name=DEC_2000_SF3_U&-_lang=en&-_sse=on&-geo_id=05000US18095


 ties (Indiana) then take Worksheet Quiz 2




000_SF3_U_DP3&-ds_name=DEC_2000_SF3_U&-_lang=en&-_sse=on&-geo_id=05000US18095
000_SF3_U_DP3&-ds_name=DEC_2000_SF3_U&-_lang=en&-_sse=on&-geo_id=05000US18097
                       Higher Education by Country
             30
             25


Percentage
             20
             15
             10
             5
             0
                  Canada   France   Germany    Italy    Japan    United   United
                                                                Kingdom
                                              Country
United
States
Worksheet 2 Data Curve

          Build Worksheet 2 Data: Use this data to construct a data curve.

          Construct a data curve showing the average level of depression reported by patients on differing doses of Prozac
          Relationship of Dose to Level of Depression
                                   Dose in mgs      Beck Depression Scale
                                         0                     30
                                        25                     28
                                        50                     15
                                        75                     20
                                       100                     30
          Source: Data is simulated

          Check Data: Use the following data to check that you know how to create a correct data curve and in Sample Work
                                                   Contingent Payment       Standard Treatment
                          Days of Drug Free Urine Frequency (Percent)       Frequency( Percent)
                                                 0                       14          19
                                               1-4                       10          20
                                               5-8                       13           0
                                              9-11                        3           2
          Source: http://www.drugabuse.gov/pdf/monographs/25.pdf page 56

          Worksheet Quiz 2 Data:

          Create a data curve showing number of accidents as a function of blood alcohol level then take Worksheet 2 Quiz
                               Blood alcohol level Accidents for which driver was culpable
                               <50                                        20
                               50-79                                      15
                               80-149                                     58
                               >=150                                      80
          Source: http://www.grotenhermen.com/driving/bates.pdf page 231
ffering doses of Prozac




urve and in Sample Worksheet 2 Quiz




n take Worksheet 2 Quiz
Worksheet 2 Time Series

          Build Data: Use this data to build a time series graph

          Construct a times series showing income by year
                     Per capita personal income
                     Year        Income
                           1993      21220
                           1994      22056
                           1995      23063
                           1996      24169
                           1997      25298
                           1998      26240
                           1999      27002
                           2000      28369
                           2001      29975
                           2002      27563
          Source: Data is fabricated


          Check Data: Use this to construct and Time Series graph and for Sample worksheet 2 Quiz
          Pedestrians crashes in New Orleans 14+year olds
                       Study       Year       Total
                       period
                     Baseline      1990        844
                                   1991        848
                                   1992        861
                                   1993        799
                                   1994        837

          http://www.nhtsa.dot.gov/people/injury/alcohol/PedestrianAccident/Main_report.html

          Worksheet Quiz 2 Data

          Construct a Time Series Graph for the data below and take Worksheet 2 Quiz
          Reported AIDS Infections In Madison County Indiana
                     Year       Frequency
                            1992         378
                            1993         755
                            1994         718
                            1995         518
                            1996         645
                            1997         555
                            1998         482
                            1999         347
                            2000         360
                            2001         360
          Source: http://www.cdc.gov/hiv/stats/hasrsupp83/table1.htm
Worksheet 2 Scatterplot

          Build Worksheet 2 data
          Construct a scatterplot showing the relationship of the weight of shoes to time to complete race
          Here are weights of the contestant shoes in grams per shoe and times in seconds
                       Contestant           Weight        Time
                                          1           382          58
                                          2           395          59
                                          3           375          54
                                          4           400          53
                                          5           402          61
                                          6           389          61
                                          7           410          63
                                          8           420          65
                                          9           378          57
                                        10            375          59
                                        11            368          53
                                        12            369          54
                                        13            381          58
                                        14            382          57
          Source: Simulated

          Check data: Use the data below to check that you are able to create a scattergram

          Relationship of Blood Alcohol Content and Driving Impairment in Women
                          BAC                Score
                                    0.025        13.73
                                     0.05        18.75
                                    0.075        23.78
                                       0.1       28.81
                                     0.15        38.86
                                       0.2       48.91
          Source http://www.mass.gov/mdaa/mvcrimes/Psychophysical%20tests%20for%20DWI.pdf


          Worksheet Quiz 2 Data

          Construct a scatterplot showing the relationship between the # of sexual partners and self-esteem
                       # of partners        Self esteem
                                          2            23
                                          4            22
                                          6            21
                                          8            17
                                        20              5
                                          5            23
                                          1            30
                                          0            25
                                          2            22
                       Source: Simulated
complete race




s and self-esteem
Worksheet 2 Frequency Polygon and Ogive

          Build Worksheet 2 Data: Use this data to build a Frequency Polygon and Cumulative % Ogive
          Students in an anthropology class received the following scores on the first test
          The scores are grouped into intervals for the sake of a clearer display.
                                                          Cumulative Cumulative
                     URL        Midpoints Frequency Frequency                %
                           22.5          15             0             0         0%
                           37.5          30           22             22        29%
                           52.5          45           35             57        74%
                           67.5          60           15             72        94%
                           82.5          75             5            77       100%
                           97.5          90             0            77       100%
          Source: Simulated


          Check Data use this data to build a Frequency Polygon & Ogive & for Sample Worksheet 2
          Monthly Mortgage Costs in Indiana (approximate)
                    URL         Midpoint                Cumulative Cumulative
                    Payment Payment Frequency Frequency               %
                           250            0           0             0        0%
                           500         250        98114        98114       10%
                         1000          750      516,739      614853        63%
                         1500         1250      253,798      868651        89%
                         2000         1750        72753      941404        96%
                         2500         2250        36875      978279       100%
                         3000         2750            0      978279       100% This category is not accurate
          Source: Adapted from http://censtats.census.gov/data/IN/04018.pdf#page=2

          Worksheet Quiz 2 Data

          For the data below construct a Frequency Polygon and Ogive and answer the questions in
          Worksheet Quiz 2.                  Data represent ages of people in US.
                                                          Cumulative Cumulative
                     URL          Midpoint Frequency Frequency              %
                                0          0            0             0        0%
                             4.5           2     423,215        423,215        7%
                            14.5          10    1309904       1,733,119       27%
                            24.5          20      879213      2,612,332       40%
                            34.5          30     831,125      3,443,457       53%
                            44.5          40     960,703      4,404,160       68%
                            54.5          50     816,865      5,221,025       80%
                            64.5          60      529844      5,750,869       88%
                            74.5          70     395,393      6,146,262       95%
                            84.5          80     265,880      6,412,142       99%
                            94.5          90       91,558     6,503,700     100%
                           104.5        100             0     6,503,700     100%
          Source: Significantly adapted from http://censtats.census.gov/data/IN/04018.pdf#page=2
gory is not accurate
Basic Statistics                                                                                      Raw        Deviation       Std    z-score
                                              Symbolic            Function Computed  Excel   Score   Scores Mean  Score          Dev         Z=
                                                                                                                               2
Name                              Symbol       Formula             Name     Formula Function Number    X     x    X - x (X - x)     S   (X - x) / S
                             Sum    SX   X1 + X2 + X3 . . . + Xk    SUM                            1     11
  Sample Size or Population Size n or N               n or N =    COUNT                                  10
            Degrees of Freedom      d.f.                   n-1                                            9
     Sample or Population Mean x or m sum/number = SX/n          AVERAGE                                  8
                            Mode Mode                 Mode = MODE.SNGL                                    7
                          Median Median              Median =     MEDIAN                                  6
                        Minimum     Min            Minimum =        MIN                                   5
                       Maximum      Max           Maximum =         MAX                                   4
                           Range Range    Range = Max - Min                                               3
                 Sum of Squares     SS   S(X - )2 or S(X - m)2 SUM, DEVSQ                                 2
                Sample Variance     S2               SS/d.f. =     VAR.S                                  1
     Sample Standard Deviation       S             (SS / d.f.)  STDEV.S                                  5
             Population Variance     s2            S(X - m)2/N     VAR.P                                  4
   Population Standard Deviation     s            (S(X-m)2/N)   STDEV.P                                  6
        Intermediate Calculation                            S/                                            6
   Sample Coefficient of Variation Cvar            (S / )*100

                                       Check Data                      5
                                       Use to check work               6
                                       and with                        7
                                       Sample Worksheet                8
                                       3 Quiz                          9
                                                                       8
                                                                       7
                                                                       6
                                                                       5
                                                                       4
                                                                       3
                                                                       2
                                                                       1
                                                                       2
                                                                       3
                                                                       4
                                                                       3
                                                    Cvar =         49.05
                                             Last Z score =        -0.79

Worksheet Quiz 3 Data                        Reebok             Nike
Create two separate worksheets                 523              925
Enter the data from column in each             632              656
Answer the questions in                        529              424
Worksheet 3 Quiz                               828              365
Each value represents the                      323              656
total dollar sales for that brand in          1101              895
one store for one week.                        675              878
                                               525              525
                                               987              969
                                               564              858
                                               636              941
                                               656              793
                                               785              354
                                               778              636
                                               454              787
                                               565              565

                                                           11
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                                                            6
Binomial Distribution                                                                           Function or
                                                              Name        Symbol      Value      Formula
                                                          Successes             X=          2
                                                              Trials            n=          3
                            Probability of one success from one trial           p=        0.5
                                  Cumulative (True) or Point (False)     Cumulative     TRUE
                       Probability of X or fewer successes in n trials     P(<=X) =             BINOM.DIST
                  Probability of greater than X successes in n trials      P(> X) =             = 1 - P(<=X)
                                  Cumulative (True) or Point (False)          Point    FALSE
                        Probability of exactly X successes in n trials      P(=X) =             BINOM.DIST
      Probability of other than X successes in n trials: Compliment        P(/=X) =             = 1 - P(=X)


                           Check Data: use to check work and Sample Worksheet 5 & 6 Quiz
                                                                         X=            5
                                                                         n=            8
                                                                         p=          0.2
                                                                Complement       0.9908

Worksheet 5 & 6 Quiz Data: Complete Worksheet 5 with the data from the problem below
An employer is accused of discriminating against applicants from Purdue.
Using an applicant pool in which 20% of those who apply are from Purdue,
in the last 10 hires only one Purdue graduate has been selected.
You do not need to revise the graph. Discriminate between proportions and percents.

                                                                    2
                                                                    3
                                                                  0.5
    0                      1          2     3
0.125            Likelihood of Girls in Family of 3
                       0.375      0.375 0.125

                             Children
                                          0.375           0.375
               0.400
 Probability




               0.300
               0.200     0.125                                     0.125
               0.100
               0.000
                              0               1                2    3
                                              Number of Girls



                                  n!
                   P( X )        0.375       * p X * q n X
                              (n  X )! X !
Poisson Distribution
                                                                                 What are you given? Use only one column.

                                                                       Occurrences and Units       Mean (l)
                                      Total number of occurrences in all units =        900
                                                            The number of units =      7000
 The specific number of occurrences that are of interest in one unit =        X=           2                  3
                                  Mean = Total Occurrences/Units              l=                              4
                                  Cumulative (True) or Point (False) =     T or F ?    TRUE         TRUE
             Probability of a score at X or below: Area at and below =    P(<=X;l)
                      Probability of a score above X = Area Above =        P(>X;l)
                                 Cumulative (True) or Point (False) =     T or F?      FALSE        FALSE
                                         P(=X;l) = Area at the Point =     P(=X;l)
             P(/=X:l) = Complement = Area everywhere except point         P(/=X;l)

This worksheet has data from 3 separate problems.
Problem 1: If in 7000 MP3 players you have 900 pieces missing what is the likelihood that any one will have 2 pieces missing
Problem 2: If the average number of customers per hour is 4 what is the likelihood that you will have exactly 3 in one hour?
Problem 3: If the likelihood of having Herpes is .20. If you have a group of 40 people what is the likelihood of 5 or fewer having

Check Data:. Use to check worksheet and for Sample Worksheet 5 & 6 Quiz
                                     Total number of occurrences in all units =         500
                                                        The number of units =           600
                                                  Specific Outcome in sample             3             6
                                                                  mean (l) =            0.8333         5
                                                               Complement =             0.9581         0.8538


Here are some possible problems for the check data:
Problem1: If there are 600 Public 4 yr Colleges and a total of 500 death due to alcohol, how likely would one school having 3 ex
Problem 2: If the average number of dates that an AU student gets in 4 years is 5 what is the likelihood of getting 6 or less?
Problem 3: If 1% of calls received at the switchboard are wrong numbers. If AU get 300 calls how likely will 2 be wrong number

Worksheet Quiz 5&6 Data
A local social action group is attempting to determine if the number of deaths due to leukemia is unexpectedly high.
If the rate is so high that it would occur by chance less often than 0.05 they will investigate further.
The probability that any one person in the population would get the disease is .00014
The size of the local county is 38,000.
The number of cases was 12. (Remember that events that are very unlikely to occur are suspect)

                                                                                900                        0.2
                                                                               7000                         40
                                                                                  2            3             5
                                                                                               4
ven? Use only one column.
                         Function, Formula
             Probability or Explanation

                                                           e l lX
                    0.2 = probability (p)        0.0000
                     40 = unit size(n)
                       5 =X                    P( X ; l) 
                         = n*p = l
                                                              X!
                TRUE
                           POISSON.DIST
                           = 1- P(<=X;l)
               FALSE
                           POISSON.DIST
                           = 1- P(=X;l)



ne will have 2 pieces missing
have exactly 3 in one hour?
 likelihood of 5 or fewer having herpes?


                 0.01      = probability (p)
                 300       = unit size(n)
                   2       =X
                   3       = mean = (l)
                  0.7760   = Complement




ly would one school having 3 exactly?
elihood of getting 6 or less?
w likely will 2 be wrong numbers


 unexpectedly high.
Gaussian Distribution Problems
Name                         Symbol                  Explanation or Formula                       Score #1
Raw score                      X                                             Given information 35.0000
Mean of Distribution            or m                                         Given information 40.0000
Standard Deviation           S or s                                          Given information       6.0000
Population Size                N           Total number of scores in the distribution (optional)        750
Deviation Score               X-                                                      X-x =
z-score                        z                                                   (X - x) / S =
                                                       Function or Formula                        Area
Probability below              p                                                NORM.S.DIST
Probability above             1-p                                                          1-p =
                                                                                                  Number
Number of scores below         #                                                         N*p=
Number of scores above         #                                                    N * (1 - p) =

                                       Check Data and Sample Worksheet 7 Quiz Data
                                                                                                Score #1
                                                                                          X=          270
                                                                              Mean = SX / n =         250
                                                                                 Std. Dev. =           10
                                                                                         N=           400


                                       Worksheet 7 Quiz Data
                                       You are selling for a sunglasses company. You visit retailers each day and obtain orde
                                       Some days you are very successful, others not.
                                       On a given day you sell only 400 dollars worth of glasses.
                                       Average daily sales for all representatives on all days in your company are mean $575
                                       The standard deviation for sales for all reps on all days is $95.
                                       The boss accuses you of goofing off. You think this is an unfair accusation.
                                       On how many of the 200 working days each year can you be expected to sell
                                       400 dollars or less assuming you are an average sales representative?

                                                                                                  35.0000
                                                                                                  40.0000
                                                                                                   6.0000
                                                                                                      750
             Score #2       Explanation or Formula
               46.0000 The second score (optional)
                       Cell reference to Column D
                       Cell reference to Column D           0.094092609
                                                                                                         ( X m )
                                                                                                                    2
                       Cell reference to Column D
                                                                                            1        
                                                           f ( x; m , s )                                 2s
                                                                                                                2
                       =X-x
                       = (X - x) / S
                                                                                                 e
             Area           Area between 2 scores                                   s 2
                                                          Estimate for 0 <= z <=1
             Number         Number between 2 scores                    0.5              1
                                                                                               1 3
                                                          q( x)  0.5  (2 ) ( z      2
                                                                                                  z )
                                                                                                7
             Score #2 Between 2                           Estimate for Z >1
                   279                         0.0209

                          Between 2
                                                      8
                                                          (1  z ) ( z ) /(1  z  z 2 )

tailers each day and obtain orders.


n your company are mean $575

an unfair accusation.
you be expected to sell
s representative?

                46.0000
         ( X m )
                    2
     
           2s
                2
 e




(1  z  z 2 )
Worksheet 7B            Gaussian Distribution from Area (p) (or Number of Scores (#)) to cutoff       Information given?
Name                                                                                         Symbol Proportion
Mean                                                          Sample or Population Mean        or m     258
Standard Deviation                               Sample or Population Standard Deviation S or s =            5
# of scores of interest                           Number of scores in the area of interest        #=
Total N of scores           Total number of scores represented by the entire distribution        N=
Area of interest               Proportion of the area of the curve below point of interest        p = 0.1000
Critical Vallue                     NORM.S.INV gives the z-score associated with area             z=
Precision                                          Multiplying z*S yields the interval width  z*S=
Absolute Precision                                            Absolute Value of Precision |z * S|
Lower Cutoff                                                              Mean - precision       X=
Upper Cutoff                                                             Mean + precision        X=




                        Check work with extra data set below
                                                                         Mean (x or m)= x or m                24
                                                            Standard Deviation (s or S) =   s or S             3
                           Total number of scores represented by the entire distribution =   #
                                            Proportion of the area of the curve of interest N
                                                             Number of scores in an area p = # / N           0.12
                                                   X = Cutoff score = Deviation - Mean =     X              20.48
                                                  X = Cutoff score = Deviation + Mean =      X              27.52


Worksheet 7 Quiz Data
John wants to play college basketball. His height is 75.3 inches
He will not be considered unless of the males graduating in his year he is in the group the tallest 9000
In a given year the number of males who graduate from high school in the USA is 175,000
Heights are distributed in a Gaussian Distribution with a mean of 71.2
The standard deviation of the heights is 2.4
What is the shortest that someone can be, if they are going to make the group of the tallest 9000?

                                                                                                             258
                                                                                                               5


                                                                                                           0.1000
Information given? Formula or
       # of scores      Function
                 30
                   6
              1750
             20000
            0.0875 = # / N
                     NORM.S.INV
                     =z*S
                     ABS
                     = (X - x) - x
                     = (X - x) + x




               72
               15
              250
             6500

            45.47
            98.53




               30
                6
             1750
            20000
Sampling Distribution Problems
Name                           Symbol                    Explanation                    Score #1 Score #2
Sample mean                                                          Given information          27       29
Population mean                   m                                  Given information          30       30
Population Standard Deviation  S or s                                Given information           5        5
Size or each sample                 n                                Given information          22       22
Population Size                   N        Number of Samples (optional information)            200      200
Deviation Score                     -m                           Distance of x from m           -3       -1
Square Root of n                 √n                    Square root of the sample size       4.6904   4.6904
Standard Error of the Mean      S / √n    Spread of the Distribution of Sample Means        1.0660   1.0660
z-score                           Z                  Deviation Score / Standard Error      -2.8142  -0.9381
                                                     Function or Formula                   Area     Area
Probability below                p                                      NORM.S.DIST
Probability above               1-p                                            (1 -p) =
                                                                                         Number    Number
Number of means below x           #                                             N*p=
Number of means above x           #                                       N * (1 - p) =


                                         Check work with extra data set below
                                                                                        Mean #1 Mean # 2
                                                              Sample mean = x =                45      46
                                                              Population Mean = m =            47
                                                 Population Standard Deviation = s =            6
                                                                  Sample size = n =            31
                                                               Population Size = N =          500


                                      Worksheet 7 Quiz Data
                     You have developed a variety of neighborhood self-help groups.
                       The average age of all groups (both Senior and not Senior) is          56
                                                                  The group size is            8
                                  The standard deviation of age of all the groups is           9
                                               The total number of groups in the city        312
                          Senior groups are defined as having an average age over             60

                                                                                              27        29
                                                                                              30
                                                                                               5
                                                                                              22
                                                                                             200
Explanation
The second mean (optional)
Cell reference to Column d
Cell reference to Column d
Cell reference to Column d
Cell reference to Column d
=     -m
= n^.5
= S / √n
= ( - m) / s
Area between 2 scores


Number between 2 scores




Between 2
                      0.1450

Between 2
                             72
Confidence Interval for the Population Mean
                                        Is my standard deviation based on a population or sample?
Name                             Explanation or Formula Symbol Population               Sample
Sample Mean                         Given Information                 1022.0000
Standard Deviation                  Given Information          s or s   57.0000
Sample Size                         Given Information               n         25
Confidence Level                    Given Information             CI          95
Degrees of Freedom                           n-1                 d.f.
Square Root of Sample Size                    n^.5                n
Standard Error of the Mean                   s / n               s
Area in tails as %                         100 - CL                %
Area in 2 tails as proportion              % / 100                  a
Area in one tail                              a/2               a/2
                                 Function or Formula          Dist. =     Z                 t
Critical Value                     NORM.S.INV, T.INV            C.V.
Precision                                  CV * s
Absolute value of Precision                  ABS
Lower Confidence Limit                    - |precision|         LCL
Upper Confidence Limit                   + |precision|          UCL
Interpretation: The population mean will fall between the LCL and UCL in the specified % of such intervals.

                                 Check data & for Sample Worksheet 8 Quiz
                                          56              55        60                      69
                                          61              56        61                      41
                                          55              58        58                      39
                                          58              59        54                      54
                                          59              51        63                      71
                                          52              42        69                      55
                                          59              59        42                      57
                                          54              58        41                      65
                                                           CI =         95
                                                         UCL =       53.07                       58.86


                                 Worksheet 8 Quiz Data
                                 Cell phone bills in dollars for a sample of people.
                                          45               30         52            73
                                          35               30         49            39
                                          32               35         48            81
                                          31               85         51            54
                                          66               90         50            56
                                          72               40         47            59
                                          47               50         54
                                          56               51         62
                                 Compute summary statistics using functions
                                 then compute the 95% confidence interval


                                                                                             1022.0000
57.0000
    25
    95
n or sample?
                         Explanation
               Cell reference to D
               Cell reference to D
               Cell reference to D
               Cell reference to D
               Used only with t
               Needed to compute sx
               Needed to compute precision
               Used to compute a

               Used with Z & t
               Distribution
               Function yields cutoff
               Area on either side of mean
               Makes sure it is positive
               Cutoff below mean
               Cutoff above mean
of such intervals.
    One sample test of mean           Formula, Function                                      Distribution
           Name                        or Explanation                    Symbol                  Z
                                             Is population standard deviation (s) known?       Yes
Sample Mean                                Observed                                                   10.7
Population Mean                    Hypothesized (expected)                           m                12.3
Standard Deviation                  Population or Sample                        s or s                 4.3
Sample Size                           Number of scores                               n                  15
Acceptable risk                          Type 1 error                                a                0.05
Deviation                          Observed-expected diff.                         -m
Square Root of sample size                   n^.5                                   n
Standard Error of the Mean         Standard deviation /  n                       sx
Degrees of Freedom                           n-1                                   d.f.
Test Statistic                     Deviation / standard error                    z or t
Absolute Value                               ABS                                  |TS|
Negative of AV                             -1 * |TS|
                                                                           Distribution         Z
1 Tailed probability                  NORM.S.DIST, T.DIST                            p1
2 Tailed probability                      2*p1                                       p2
Confidence Intervals
Area in one tail                             a/2                                   a/2
Critical Value                        NORM.S.INV, T.INV                            C.V.
Precision                                 CV * sx
Absolute value of Precision                 ABS                                |CV * sx|
Lower Confidence Limit                  x - |precision|                            LCL
Upper Confidence Limit                  x + |precision|                            UCL


            Tails                            2 Tails                  1 tail right          1 tail left
       Null Hypothesis                     H0: m = 130               H0: m <= 130          H0: m >= 130
    Alternate Hypothesis                   H1: m /= 130              H1: m > 130           H1: m < 130

Check data & for Sample Worksheet 9 Quiz
Sample Mean                              Observed                                                       30
Population Mean                   Expected or Hypothesized                            m                 26
Standard Deviation                  Sample or Population                         s or s                  9
Sample Size                           number of scores                               n                  32
                                                                               Alpha +                0.05
2 Tailed probability                           2*p1                                  p2             0.0119



Worksheet 9 Quiz Data           DO NOT ASSUME these are in order for coping and pasting.
The average sales per day for your company (which has 1500 stores) are
The number of stores using your AU strategy are
Sales per day for the stores using the AU strategy are
The standard deviation of the stores using the strategy is
                                                                                                Alpha =
You would like to impress the boss that the AU strategy is not just producing a chance improvement
but a statistically significant improvement. Do the necessary statistical analysis and draw your conclusions.

                                                                                                   10.7
                                                                                                   12.3
                                                                                                    4.3
                                                                                                     15
                                                                                                   0.05
 t       Explanation
No
         Cell reference from D
                                               X  mH
                                           t X  m H 0 0 sˆ sˆ X  s
         Cell reference from D                                         s
                                          t
                                                sˆ sˆ X
         Cell reference from D
                                                                      nn
                                                              X
         Cell reference from D                      X
         Used with T.INV
         Should be the same for Z and t
         Should be the same for Z and t
         Should be the same for Z and t
         Used with T.DIST and T.INV
         Should be the same for Z and t
         Used with Z and t
         Used with Z and t
 t       Tails
         1
         2


         T.INV uses E20 & E12
         Area on either side of mean
         Makes sure it is positive
         Cutoff below mean
         Cutoff above mean




         If p <= a then reject H0




0.0173                         2
             $4,500
                  25
              $5,100
              $1,200
                0.05

our conclusions.
                   Two Sample Mean Test
                          Name                                    Formula or Function
                                            Sample Means                                      1   -    2

                              Population Means (optional)                                 m1 - m2
            Deviation of observed difference from expected                 (x1 - x2) - (m1 - m2)
                                       Standard deviations                                S or s
                                                                                        S or s2
                                                                                          2
                                                  Variances
                                             Sample sizes                               n1 + n2
                                       Degrees of freedom         df1+ df2 = (n1 - 1) + (n2 - 1)
                   Unequal Sample Size Correction Factor                             1/n1 + 1/n2
                                         Sum of Squares                       df1*S12+df2*S22
                            Pooled Variance of Difference                             SS/d.f.
                   Adjusted Pooled Variance of Difference                         SS/d.f.*CF
                                              Variance / n                       S12 /n1 + S22/n2
                                  Smaller of d.f.1 or d.f.2 =                                         IF
                                                                       (S1 /n1) + (S2 /n2)]
                                                                             2                2
     Std. error col. D for Z & t unequal col. H for t equal
                            Test Statistic [t (unequal) or z]       deviation / standard error
                          Absolute Value of Test Statistic                               ABS
                                Negative of absolute value                           -1 * |TS|
                                         Are the population standard deviations (s's) known?


        1 Tailed probability (area of the curve in one tail) NORM.S.DIST T.DIST T.DIST
    2 Tailed probability (area of the curve in both tails)               2 * p1
Confidence Intervals
Type one error                                                                                alpha
Area in one tail                                                           a/2
Critical Value                                                  NORM.S.INV, T.INV, T.INV
Precision                                                                CV * sx
Absolute value of Precision                                                ABS
Lower Confidence Limit                                                x - |precision|
Upper Confidence Limit                                                x + |precision|


                           Tails                                       2 Tails
                     Null Hypothesis                                 H0: m1 = m2
                   Alternate Hypothesis                              H1: m1 /= m2
                                                        Check Data & for Sample Worksheet 10A Quiz Data
                                                                                    1   -    2
                                                                                   m1 - m2
                                                                      (x1 - x2) - (m1 - m2)
                                                                                    S or s
                                                                                 S2 or s2
                                                                                  n1 + n2




Worksheet 10A Quiz Data
You are attempting to determine weather your athletes will perform better if they consume Gatorade or water.
You divide your sprinters into two groups and have one group pre-load on Gatorade and the other pre-load on water.
You then have them run a 400-meter race and record the average time of the two groups.
    The average time for the Gatorade was in seconds = 47
        The average time for the water was in seconds = 49
        The standard deviation for the Gatorade group = 5
            The standard deviation for the water group = 4
                               The size of both groups = 17
                                                 Alpha = 0.05
You may assume the population standard deviations, although unknown, are equal.
(Be careful in running lower times are better)

Welch's Approximate Method for CI when there is heterosedasticity
s2 a                                                                                    0.0
na                                                                                          15
na-1                                                                                        14
dfw                                                                 #DIV/0!
MEw                                                                 #DIV/0!
LCL                                                                 #DIV/0!
UCL                                                                 #DIV/0!
                 Symbol               Group 1                   Group 2                  Difference
                                                    73.00 -               68.00 =
                                                            -                        =


                                                    18.00                 10.00


                   N                                   15                      11            Sum ↓
                 d.f.total                                  +                        =                    ← t equal
                   CF                                       +                        =                    ← t equal
                   SS                                       +                        =                    ← t equal
                                                                                                          ← t equal
                 s2 1-    2                                                                               ← t equal
                                                            +                        =                    ← z & t unequal
                        d.f.smaller                             ←t unequal                  t equal ↓
                 s 1- 2                                         ← z & t unequal                           (SS/d.f.)*CF]
                   TS                                           ← z & t unequal                           ← t equal
                  |TS|                                                                                    ← t equal
                                                                ← z & t unequal                           ← t equal
s's) known?                                 Yes                No, are s's equal?           Default
                                                                    No                          Yes 
                                             Z                   t (unequal)                t (equal)                   Tails
                   p1                                                                                                    1
                   p2                                                                                                    2

                                a                    0.05                     0.05                        cell reference to D26
                        a / 2 for z                                       0.025                           a / 2 for t
                              C.V.                                  #DIV/0!                               T.INV df from H9
                 Use D28 & D16                                                                            =H16*H28
                      |CV * sx|                                     #DIV/0!                                             ABS
                              LCL                                   #DIV/0!                                   x     - |precision|
                              UCL                                   #DIV/0!                                   x     - |precision|


               1 tail right              1 tail left
              H0: m1 <= m2              H0: m1 >= m2
              H1: m1 > m2               H1: m1 < m2
le Worksheet 10A Quiz Data
                                                   45.00 -            52.00
                                                           -

                                                   21.00              24.00
                                                   441.0              576.0
                     N                                32                 21

                                           Z                   t (unequal)    t (equal)
                             p1                0.1378             0.1442       0.1337
                             p2                0.2755             0.2885       0.2673


ey consume Gatorade or water.
orade and the other pre-load on water.




            s2 b                                     0.0
            nb                                       11
            nb-1                                     10
            t                            #DIV/0!




                                                   73.00 -            68.00
                                                         -

                                                   18.00              10.00

                                                     15                  11
             Effect Size                                  Function
                                    1   -   2)
Absolute value of difference                              ABS
                                    2        2
                                    S +S
                                2
                       (S1 + S22)/2

                   (√(S12 + S22)/2)                       SQRT
                            2           2
         1   -   2)/(√(S1       + S2 )/2)                 =d          Cohen's D
                                       d2
                                   d2 + 4
                                √(d2 + 4)
                       d / √(d2 + 4)                      = rΥλ       Effect size correlation
Effect Size Explanation                          http://www.uccs.edu/~faculty/lbecker/es.htm
      F Test

                                                                                        Standard Deviations
     Name                           Function or Formula                  Symbol            Group 1
       Sample sizes                  Given information                     n                        25
Standard Deviations                  Given information                      S                     6.70
Degrees of freedom                          n -1                            d.f.
               Variance      S^2 or given information in F & G              S2
                                                                                            Larger
                                                                              2
          Variance                           IF                             S
Degrees of freedom                           IF                             d.f.
                                          SL / SS2
                                            2
Test Statistic: F Test                                                       F
                                                                                             P(F)
 Probability in 1 tail                  F.DIST.RT                           p1
Probability in 2 tails                    2 * p1                            p2

       Tails                                2 Tails                     1 tail right       1 tail left
  Null Hypothesis                        H0: s21 = s22                 H0: s21 <= s22    H0: s21 >= s22
Alternate Hypothesis                    H1: s21 /= s22                 H1: s21 > s22      H1: s21 < s22

                          Check Data & Sample Worksheet 10 AB Data                             Group 1
                                                 Sample size = n =                                  24
                                         Standard Deviations = S =                                5.30
                                                  Variances = S2 =
                                           Probability for 2 tails =                               0.0359



                          Worksheet 10 AB Data
                          It is the 4th quarter,                          Jones              Green
                          your basketball team is down 94 to 96.             2                 1
                          There is no time left on the clock.                0                 2
                          A technical foul has been                          2                 1
                          called against your opponent.                      2                 2
                          Your team will get two shots.                      0                 0
                          Below are the number of shots your                 0                 1
                          best two free throw shooters                       2                 2
                          have made out of 2 in the                          2                 1
                          last 18 two-shot foul game situations.             0                 1
                          Which player will you choose and why?              2                 1
                          Alpha = .05                                        2                 1
                                                                             0                 1
2   1
2   2
0   1
2   1
0   2
2   1

          25
        6.70
         What am I given?


dard Deviations      Variances
           Group 2 Group 1 Group 2
                                                s L
                                                    2
                  20       25    23         F 
                9.45                            s S 2



                       44.89    89.30
         Smaller   Larger    Smaller




           Tails      P(F)      Tails
             1                   1
             2                   2




         Group 2 Group 1 Group 2
                29     24      20
              8.20
                       32.12     43.98
             2         0.4688           2
  20     25      23
9.45

       44.89   89.30
           Dependent t test
                Name                             Formula or Function         Symbol             Value
                                 Means               AVERAGE
          Sample Standard Deviations                  STDEV.S                  S

               Mean of the differences               AVERAGE
         Expected difference (if given) Expected difference (if given)         m
                              Deviation                   -m

 Standard Deviation of the Differences                STDEV.S                  SD

                           Sample size                COUNT                    np
          Square Root of Sample Size                    np^.5                 np
     Standard Error of the Differences                S /  np                 sD
                  Test statistic: t-test      deviation / standard error        t
      Absolute value of Test statistics                  ABS                   |t|
                     Left tail value of t                |t|*-1                -t
                   Degrees of freedom                  np -1 =                d.f.D
                                                                                                 P(t)
                 1 Tailed probability                 T.DIST                   p1
    2 Tailed probability (both tails)                  2*p1                    p2
Confidence Intervals
Area in tails                                             a                              a              0.05
Area in left tail                                        a/2                           a/2
Critical Value                                          T.INV                         C.V.
Precision                                              CV * sD
Absolute value of Precision                              ABS                  |CV * sD|
Lower Confidence Limit                          deviation - |precision|           LCL
Upper Confidence Limit                          deviation + |precision|           UCL


              Tails                                 2 Tails                1 tail right 1 tail left
         Null Hypothesis                           H0: m1 = m2             H0: m1 <= H0: m1 >= m2
                                                                                m2
      Alternate Hypothesis                         H1: m1 /= m2             H1: m1 >         H1: m1 < m2
                                                                               m2

                                            Check Data & Sample Worksheet 10C Data

                                                      Group 1                Group 2

                                                          26                   24
                                                          25                   22
                                                          22                   21
               21                 23
              29                  24
              31                  29
              32                  17
              29                  19
     Probability for 1 tail        0.0265
     Probability for 2 tails       0.0531


Worksheet 10C Data
You wish to see if cholesterol scores on an old diet
are higher than cholesterol scores on an new diet.
You measure ten individuals before and after 1 month on the diet.
 alpha = .05
       Individual Diet             Old             New
               1                   300             301
               2                   285             281
               3                   310             300
               4                   267             250
               5                   309             300
               6                   293             345
               7                   310             301
               8                   267             232
               9                   325             302
              10                   301             300

                                        16               11
                                        12                5
                                        17               11
                                        12                7
                                         5                4
                                         6               10
        X        X                                Effect Size                                   Function
Group       1        2        D                                         1   -   2)
                          Difference          Absolute value of difference                      ABS
                           X1 - X2 ↓                                  S12
            16       11                                                     S22
            12       5                                                S12 + S22
            17       11                                      (S12 + S22)/2

            12       7                                   (√(S12 + S22)/2)                       SQRT
                                                                  2         2
            5        4                        1   -   2)|/(√(S1       + S2 )/2)                 =d
            6        10                Effect Size Explanation                       http://www.uccs.edu/~faculty/lbecker/es.h




                                               D  mD
Tails                                  tD    
  1                                            SD
  2
                                                   nD
month on the diet.
             Cohen's D
.uccs.edu/~faculty/lbecker/es.htm
      Pearson Correlation                   Formula or                                                      3↓   4↓
             Name                            Function                Symbol          Value            X    X-    ZX
          Mean of X, Y                      AVERAGE                    ,                        1→
 Sample Standard Deviation of X, Y          STDEV.S                    S                        2→
         Sum of ZxZy =                         SUM                   SZxZy                    ←8      43
          Sample Size                    number of pairs               n                      ←9      48
    Degrees of freedom for r                    n-1                   d.f.1                   ←10     56
  Pearson Correlation Formula              SZXZY / (n -1)               r                     ←11     61
  Pearson Correlation Function               CORREL                     r                     ←12     67
    Degrees of freedom for t                 n - 2 for t              d.f.2                   ←13     70
    Coefficient of Determination                  r2                    r2                    ←14
                                                        2                   2
  Coefficient of Non-determination             1-r                      k                     ←15
                                               df2/k2                                         ←16
        Square Root of C13
                                                    2
                                             (df2/k )^.5             df2/k )   2
                                                                                              ←17
                                                            2
    Test Statistic: t for Pearson            r*(df2/k )                 t                    ←18
        Absolute value of t                     ABS                     |t|                   ←19
               left tail                        |t|*-1                  -t
                                                                                     P(t)     Tails
        1 Tailed probability            T.DIST, d.f.2 = n-2             p1                      1
        2 Tailed probability                   2 * p1                   p2                      2
        H0: r = 0; H1: r /= 0        if p2 <= a then reject H0

Check data &                                                     5         2
Sample Worksheet 11A Data                                        6         5
                                                                 3         3
                                                                 7         1
                                                                 8         2
                                                                 2         5
                                                                 4         7
                                                  |t|                 1.4289 ←19
                                                                       P(t) Tails
                                                 p1                   0.1062    1
                                                 p2                   0.2124    2

Worksheet 11A Data                                                   Bonus Products
Assume that you are testing to see                                      0.0    1.25
if there is a relationship between the amount                           0.1    1.35
of bonus/hr. and products sold /hr. Use a = .05.                        0.2    1.40
                                                                        1.0    1.65
                                                                        1.5    1.70
                                                                        2.0    1.80
                                                                        2.5    1.85

                                                                                43      128
                                                                                48      120
56   135
61   143
67   141
70   152
       5↓   6↓    7↓
Y     Y-    ZY   ZxZy


128
120
135
143
141
152
          Spearman Correlation                          Function                                                    RANK.AVG
                      Name                            or Formula          Symbol          Value     Score   X       Rank of X
                       Acceptable Risk             Given information           a             0.05    1          1
Sum of the squared differences in ranks                 SUM                   Sd2                    2          2
                                                             6*Sd2 =                                 3          3
                               Sample size            COUNT                    np                    4          4
                                                                      2
                                                                 n =                                 5          5
                                                              n2 -1 =                                6          6
                                                           n(n2 -1) =                                7          7
                                                         2
                                                      6Sd /n(n2 -1) =                                8          8
          Spearman Correlation Formula              1-6Sd2/n(n2 -1) = rs computed                    9
          Spearman Correlation Function CORREL on ranks rs computed                                  10
            Absolute Value of Spearman      ABS             |rs|                                     11
           Critical Value for rs (2 tail test)                               rs table     #N/A       12
H0: rs = 0; rs /= 0                              If |rs| computed >= rs table reject H0              13
                                                                                                     14
                                                                                                     15
Check Data and for                                                     XY                            16
Sample Worksheet 11AB                                             Score Score                        17
                                                                      52      225                    18
                                                                      45      220                    19
                                                                      61      210                    20
                                                                      51      230                    21
                                                                      36      265                    22
                                                                      38      241                    23
                                                                      42      254                    24
                                                                      54      228                    25
                                                                      53      229                    26
                                                              rs computed  -0.767                    27
                                                                                                     28
Worksheet 11AB Quiz Data                                                                             29
Physician                                Skill ranking     Income Looks Rank                         30
Jones                                                 61 150,000          90                         31
Smith                                                 87 200,000          60                         32
Doe                                                   32 75,000          109                         33
Green                                                120 60,000          155                         34
Young                                                175 190,000          36                         35
Short                                                155 50,000          180                         36
You will need to make two copies of this worksheet on separate tabs.                                 37
A group of single adults were asked to rank pictures of each                                         38
physician for attractiveness.                                                                        39
A group of nurses ranked the physicians skill.                                                       40
Information of each physician's net income                                                           41
for last year was obtained from the IRS.                                                             42
Determine if the physician's income is more closely related to             43
skill in the operating room or good looks.                                 44
                                                                           45
                                                                 1   125   46
                                                                 2    90   47
                                                                 3   110   48
                                                                 4    75   49
                                                                 5    92   50
                                                                 6    85   51
                                                                 7    65   52
                                                                 8    55   53
                                                                           54
                                                                           55
                                                                           56
                                                                           57
                                                                           58
                                                                           59
                                                                           60
                                                                           61
                                                                           62
                                                                           63
                                                                           64
                                                                           65
                                                                           66
                                                                           67
                                                                           68
                                                                           69
                                                                           70
                                                                           71
                                                                           72
                                                                           73
                                                                           74
                                                                           75
                                                                           76
                                                                           77
                                                                           78
                                                                           79
                                                                           80
                                                                           81
                                                                           82
                                                                           83
                                                                           84
                                                                           85
                                                                           86
                                                                           87
                                                                           88
                                                                           89
                                                                           90
                                                                           91
                                                                           92
                                                                           93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
      RANK.AVG            Spearman Table
Y     Rank of Y   d
                      2
                      d   N/a      0.10     0.05    0.01
125                          5    0.900    1.000
 90                          6    0.829    0.886   1.000
110                          7    0.715    0.786   0.929
 75                          8    0.620    0.715   0.881
92                           9    0.600    0.700   0.834
85                          10    0.564    0.649   0.794
65                          11    0.537    0.619   0.764
55                          12    0.504    0.588   0.735
                            13    0.484    0.561   0.704
                            14    0.464    0.539   0.680
                            15    0.447    0.522   0.658
                            16    0.430    0.503   0.636
                            17    0.415    0.488   0.618
                            18    0.402    0.474   0.600
                            19    0.392    0.460   0.585
                            20    0.381    0.447   0.570
                            21    0.371    0.437   0.556
                            22    0.361    0.426   0.544
                            23    0.353    0.417   0.532
                            24    0.345    0.407   0.521
                            25    0.337    0.399   0.511
                            26    0.331    0.391   0.501
                            27    0.325    0.383   0.493
                            28    0.319    0.376   0.484
                            29    0.312    0.369   0.475
                            30    0.307    0.363   0.467


                                           6Sd 2
                                 rs  1 
                                             
                                          n n2 1     )
Regression and Prediction Interval                                                                    Variable
                 Name                        Function or Formula     Statistic                          X
             Sample Mean                     AVERAGE for X &Y          x                     1
           Standard Deviation                STDEV.S for X & Y          s                    2
              Sample Size                     COUNT for X & Y           n                    3
 Compute Pearson & Test for Significance                                                                 X
           Pearson Correlation                    CORREL                r                    4          22
         Degrees of freedom for t                    n-2               d.f.t                 5          14
       Coefficient of Determination                    r2                r2                  6          31
                                                            2               2
     Coefficient of Non-determination                1-r                k                    7          36
                                                                2                2
        Ratio of d.f. to Coef of ND             (n - 2)/(1 - r )     d.f ./ k                8           9
           Square Root of E11
                                                            2
                                                 (d.f ./ k )^.5     (d.f ./ k )  2
                                                                                             9          41
              Test Statistic: t                 r * (d.f ./ k2)         t                  10          19
              Absolute value                        ABS                 |t|                 11
                    left tail                       |t|*-1              -t                  12
             1 tail probability =                  T.DIST               p1                  13
             2 tail probability =                   2 * p1              p2                  14
          Predict Y value from X
           Score to predict from              Given Information          X                  15   11
           Predicted Value of Y                 FORECAST                Y'                  16
    Set up Prediction Interval around Y'
   Sum of Squares of predicted scores         SUM of Column J        S(Y-Y')2               20
       Variance of predicted scores              S(Y-Y')2/d.f.                              21
        Standard Error of Estimate             (S(Y-Y')2/d.f.)^.5       se                  22
             Confidence Level                 Given Information         CI                  22   99
             Area in tails as %                    100 - CI             %                   24
        Area in 2 tails as proportion              % / 100               a                  25
      Area in one tail as a proportion               a/2                 a                  26
             Critical Value of t                   T.INV               C.V.                 27
                 Precision                         CV * se          Precision               28
        Absolute value of Precision                  ABS            |Precision|             29
          Lower Confidence Limit                Y' - |precision|       LCL                  30
          Upper Confidence Limit               Y' + |precision|        UCL                  31


                                           Check Data &                         X=     42
                                           Data for Sample                      CI =   99
                                           Worksheet 11C                 X             Y
                                                                        51             152
                                                                        45             149
                                                                        39             135
                                                                        56             161
                                                                        71             176
                                                                        82             189
                                                                   91      184
                                                                   75      165
                                                                   51      147
                                                                   se       6.44
                                                                  LCL     120.07
                                                                  UCL     165.15


Worksheet 11C Data
You have data for long distance telephone charges/month
and sales volume/month for each of your sales representatives.
Ms. Smith has reported a monthly expense of                       594
expect what limits for her sales with confidence level             99
                                              Phone charge        Sales
                                                   475           28,000
                                                   209           14,000
                                                   684           35,000
                                                   359           15,000
                                                   576           29,000
                                                   704           34,000

                                                                  22       20
                                                                  14       14
                                                                  31       54
                                                                  36       63
                                                                   9       17
                                                                  41       71
                                                                  19       23
Variable
           Y
                          alpha =    0.05          Continue with Regression

                     17       18              19
           Y    Y'         Y-Y'     (Y-Y')2
           20                20.0      400.0
                                                               n2
           14                14.0      196.0
                                                   t r*
           54
           63
                             54.0
                             63.0
                                      2916.0
                                      3969.0
                                                               1  r2

                                                          Sy  y')
           17                17.0      289.0
                                                                          2
           71                71.0     5041.0
           23                23.0      529.0       sest 
                                                            n 2
                                                   CIy'  y'±t * Sest
        1-way X2              Formula or
         Name                   Function          Symbol              Chog      Protestant RC          Other
   Frequency Observed            Given              fO                       90         45       35             15
       Sample size                SUM               n
   Proportion expected           Given              p                    0.45        0.25       0.15           0.10
   Frequency Expected        n * p or Given         fE
        Difference                                  fO - fE
   Squared Difference                             (fO - fE)2
      Cell Chi-square                            (fO - fE)2 / fE
  Number of categories           COUNT                  k
    Degrees of freedom             k-1                 d.f.
 Test Statistic: Chi-Square       SUM                  X2
         Probability         CHISQ.DIST.RT              p
H0: fO = fE; H1: fO /= fE
Retaining H0 is saying the frequencies observed do not differ from what would be expected by chance from given proportions
Rejecting H0 is saying the frequencies observed differ by more than we would expect by chance from given proportions
Effect Size
Sample size * d.f.           multiply               N*(k-1)              0
Intermediate Calculation     divide             X2 / (N*(k-1))    #DIV/0!
Cramer's Phi                 SQRT             (X2 / (N*(k-1)))^.5 #DIV/0!

                                              Check Data and Sample Worksheet 12 AB
                                                               Bush      Kerry      Nadar
                                                     fO               20         15       3
                                                     p              0.50       0.48    0.02
                                                    p=           0.0269


Worksheet 12 AB Data
You wish to determine if the proportion of Purdue, Indiana, and Notre Dame graduates
who work in your company is different from the distribution in its population of your state
                         % in state      # in company
Purdue                              82%               155             Alpha = .05
Indiana University                  12%                 35 Be sure to convert percents to proportions.
Notre Dame                           6%                 10

                                                                90           45        35        15              7


                                                               0.45      0.25        0.15       0.10           0.05
            None
                   7

                0.05




ance from given proportions
rom given proportions
4X4 2-way Chi Square    Restaurant If you have no data for a cell leave it blank do NOT use a zero.
        Class            Ruby T's       Garfields       Red Lob       Applebys
Freshman
Sophomore
                                 15
                                 25
                                                   25
                                                   26
                                                                 14
                                                                 45
                                                                                19
                                                                                43                    Fe 
Junior                           32                21            36             42
Senior                           34                24            26             24
Column Total

                                              fo           Row t        Col t




                       Rows                             Columns
                       Rows -1                          Columns -1
                       d.f.

      Hypothesis        Hypothesis          Test of     Decision     Assoication
        Null            H0 : f O = f E   Independence     Retain         No
      Alternate         H1: fO /= fE      Dependence      Reject         Yes

Check Data and Sample Worksheet 12AB Data
                             Priority
Major                  Relationship       Money
Business                          23              15
Other                             15              10
                                 p=           0.9667



Worksheet 12AB Data
Table shows the arrival time of packages
                          2 days or More than 2 days
                             less
         UPS                  32           11
       FEDEX                  35            3
Do the services differ in the # of packages delivered
in 2 days or less? Alpha = .05

                                   15                   25   14   19
                                   25                   26   45   43
                                   32                   21   36   42
                                   34                   24   26   24
e it blank do NOT use a zero.
             Row Total
                                                   RowTotal * ColumnTotal
                                        Fe 
                                                        GrandTotal
                                     Grand Total
                                                                                 Cell X2
                    Grand t               fe              fo-fe       (fo-fe)2 (fo-fe)2/fe




                                     Chi-square Sum           X2 =
                                     Probabilty CHISQ.DIST.RT p =




                d. f .  Rows  1) * Columns  1)

            Effect Size
            Phi                      2X2
            Chi-square/Sample Size   divide        X2 / N             #DIV/0!
                                    SQRT          (X2 / N)^.5        #DIV/0!
            Cramer's Phi             >2X2
            Determine k              Minimum                                 0
            Compute                  subtract             k-1               -1
            Sample size * (k-1)      multiply           N*(k-1)              0
                                                      2
            Intermediate Calculation divide          X / (N*(k-1))     #DIV/0!
                       c            SQRT          (X2 / (N*(k-1)))^.5 #DIV/0!
               Simple ANOVA                      Group Names               Shell        Gulf         Amoco
                                                       Score #     1               35          25        29
                                                       Score #     2               29          35        34
                                                       Score #     3               27          41        36
                                                       Score #     4               38          44        38
                                                       Score #     5               42          39        22
                                                       Score #     6               51          41        21
                                                       Score #     7               23                    35
                                                       Score #     8                                     33
                                                       Score #     9
                                                       Score #    10
                                                       Score #    11
                                                       Score #    12
                                                       Score #    13
                                                       Score #    14
                                                       Score #    15
Sample Size (of each group)                       COUNT            n
Total of all Sample Sizes n1 + n2 + . . . Nk       SUM             N
Number of Groups                                  COUNT            k
Sum of Squares (of each group)                    DEVSQ           SS
Means (of each group)                            AVERAGE          x
Grand Mean (of all scores)                       AVERAGE           x
Deviation                                          xj - x
Squared Deviation                                  (xj - x)2
Weighted Squared Deviation                        nj(xj - x)2
Sum of Squares Between (for all groups)        SUM Snj(xj - x)2   SSB
Sum of Squares Within (for all groups)         SUM SS(X - x)2     SSW
Sum of Square Total (of all scores)                DEVSQ          SST
Degrees of Freedom Between                           k -1         d.f.B
Degrees of Freedom Within                           N-k           d.f.W
Degrees of Freedom Total                           N-1            d.f.T
Mean Square Between                               SSB / dfB       MSB
Mean Square Within                                SSW / dfW       MSW
Test Statistics: F                               MSB / MSW          F
Probability                                      F.DIST.RT          p
                                                                  Source      SS          d.f.        MS       F
Between the Means                                   Snj(xj - x)2 Between
Within the Groups                                   SS(X - x)2 Within
Sum of Squares Total                                 SSB + SSW    Total


Hypothesis                                                                 Check work with data below
Null: H0: m1 = m2 = m3 = m4 . . = mK                                        Papa J Domino Pz Hut CiCi
Alternate: H1: At least 2 means differ                                             9             5         9       3
                                                                                   8             6         8       4
                                                                                   6             8         7       5
                                                                                   7             7         6       3
                                                                            5          5            4
                                                                            9          2            1
                                                                            8

                                                            Source    SS        d.f.       MS F
                                                             SSB       67.06        3      22.35 8.572
                                                             SSW       49.55       19       2.61
                                                             SST      116.61

You are considering 3 cities for the annual convention of your professional association
In order to determine which location is going to be the most economical for your members,
you have sampled motel rooms and prices in each of the 3 cities.
Below are the cities and the prices for the motel rooms
Is there a significant difference in the cost of a room in the 3 different cities. Alpha = .05
               Fort Wayne                       Chicago        Indy
                     75                            105          75
                     85                            130          90
                    100                            115         100
                    105                            145         125



                                                                35        25       29
                                                                29        35       34
                                                                27        41       36
                                                                38        44       38
                                                                42        39       22
                                                                51        41       21
                                                                23                 35
                                                                                   33
p
  p
0.0008
            Simple ANOVA                     Group Names                     Psy         Business
                                                   Score #            1            10            10
                                                   Score #            2             9            12
                                                   Score #            3             6             9
                                                   Score #            4             8             4
                                                   Score #            5             7             6
                                                   Score #            6             5             5
                                                   Score #            7             8             6
                                                   Score #            8             4             3
                                                   Score #            9             6             9
                                                   Score #           10             9            11
                                                   Score #           11            12
                                                   Score #           12
                                                   Score #           13
                                                   Score #           14
                                                   Score #           15
     Sample Size (of each group)             COUNT                    n
       Total of all Sample Sizes              SUM                     N
          Number of Groups                   COUNT                    k
    Sum of Squares (of each group)           DEVSQ                   SS
        Means (of each group)               AVERAGE                  x
      Grand Mean (of all scores)            AVERAGE                   x
               Deviation                      xj - x
          Squared Deviation                   (xj - x)2
     Weighted Squared Deviation              nj(xj - x)2
Sum of Squares Between (for all groups)   SUM Snj(xj - x)2           SSB
 Sum of Squares Within (for all groups)   SUM SS(X - x)2             SSW
  Sum of Square Total (of all scores)         DEVSQ                  SST
     Degrees of Freedom Between                 k -1                 d.f.B
      Degrees of Freedom Within                N-k                  d.f.W
      Degrees of Freedom Total                N-1                    d.f.T
        Mean Square Between                  SSB / dfB               MSB
         Mean Square Within                  SSW / dfW              MSW
           Test Statistics: F               MSB / MSW                 F
             Probability                    F.DIST.RT                 p
                                                                    Source   SS            d.f.
          Between the Means                      Snj(xj - x)   2
                                                                   Between
           Within the Groups                     SS(X - x)2         Within
         Sum of Squares Total                     SSB + SSW         Total
                                                                                        Group
             Eta-squared                     SSB / SST* 100           h2                Mean
                                                                                        n
                Group 1
                   vs.                                                       vs.           vs.
                Group 2
          Difference in Means                                      x1-x2
       Tukey use if n's are equal
 Absolute Value of Difference in Means          ABS                |x1-x2|
         Tabled value for Tukey for .05             q for 0.05          q                 #N/A
         Tabled value for Tukey for .01             q for 0.01          q                 #N/A
           Means Square Within / n                   MSW/n           MSW / n
   Square Root (Means Square Within / n)            (MSW/n)^.5       (MSW / n).5
          Tukey Value for a = .05                q.05 * (MSw/n)^.5     TV.05
            Tukey Value for a = .01              q.01 * (MSw/n)^.5      TV.01
      Critical Value.05: if positive reject H0   |x1-x2| - TV.05        CV.05
      Critical Value.01: if positive reject H0   |x1-x2| - TV.01        CV.01
        Scheffe use if n's are not equal
         Square of difference in mean              (x1-x2)^2         (x1-x2)2
         Reciprocal of first sample size              1 / n1            1 / n1
       Reciprocal of second sample size               1 / n2            1 / n2
             Sum of reciprocals                   1 / n1 + 1 / n2
  Product of Sum of reciprocals, dfb & MSW       =$D29*$D33*D61
                 Scheffe Value                      =d58/d62             Fs
   Probability of type 1 error in Rejecting H0     F.DIST.RT             p
Hypotheses for ANOVA
Hypothesis
Null: H0: m1  m2  m3  m4 . .  mK                                 Check work with this data
Alternate: H1: At least 2 means differ?                                               Arby's        Bob Evans
                                                                                                 12         13
Hypotheses for Tukey or Scheffe                                                                  12         15
Null: H0: m1  m2                                                                                13         14
Alternate: H1: m1 / m3                                                                       14                13
                                                                                              15                12
                                                                                              12                15
                                                                                              12                16
                                                                                              11                14
                                                                                              13                 9
                                                                                               9                12
                                                                                              12
Table is available at                                                          p=      0.5964507          0.0275641
          Tukey Table On the Web
       Critical Values for Tukey's HSD
                                                                     Worksheet 13B Quiz Data
                                                                     Determine if four brands of athletic shoe
                                                                     differ in the number of months they last.

                                                                                      A               B
                                                                                 1)              24             36
                                                                                 2)              36             48
                                                                                 3)              12             50
                                                                                 4)              11             39
                                                                                 5)               5             38
                                                                                 6)              30             42
 7)   21   46
 8)   32   37
 9)   15   47
10)    7   44

10    10   12
 9    12   13
 6     9   11
 8     4   19
 7     6   17
 5     5   13
 8     6   14
 4     3   15
 6     9   11
 9    11    9
12          6
Pol Sci            SW
          12             5
          13             5
          11             9
          19             7
          17             5
          13             9
          14             6
          15             3
          11             7
           9             5
           6




                                   Use Tukey




 MS            F             p




  vs.              vs.       vs.       vs.

                                               Both
                                                       Values for alpha = .05
                                               Tukey
                                                                   Tukey     Degrees of Freedom Within
                                                                   Tukey                              Infinity
                                                                   Tukey                                     5
                                                                   Tukey                                    6
                                                                   Tukey                                    7
                                                                   Tukey                                    8
                                                                   Tukey                                    9
                                                                   Tukey                                   10
                                                                                                           11
                                                                   Scheffe                                 12
                                                                   Scheffe                                 13
                                                                   Scheffe                                 14
                                                                   Scheffe                                 15
                                                                   Scheffe                                 16
                                                                   Scheffe                                 17
                                                                   Scheffe                                 18
                                                                                                           19
                                                                                                           20
                                                                                                           24
             Chi-Chi's      Dolinsky's                                                                     30
                          9           14                                                                   40
                          8           12                                                                   60
                          9           13                                                                  120
                          8          14
                          9          11
                         10          10
                          9          11
                         12          12
                         14          13
                         11          11
                                     12
                 0.9958222    0.0010136    0.4595344   0.0477663




ds of athletic shoe
 months they last.

             C                D
                         24          30
                         29          32
                         21          29
                         30          31
                         28          33
                         22          35
27   28
24   32
26   33
25   35

 5
 5
 9
 7
 5
 9
 6
 3
 7
 5
                             Values for alpha = .01
Degrees of Freedom Between
  1      2     3      4      5      6       7     8      9     Degrees of Freedom Within
2.77   3.31   3.63   3.86   4.03   4.17   4.29   4.39   4.47                               5
3.64   4.60   5.22   5.67   6.03   6.33   6.58   6.80   6.99                               6
3.46   4.34   4.90   5.30   5.63   5.90   6.12   6.32   6.49                               7
3.34   4.16   4.68   5.06   5.36   5.61   5.82   6.00   6.16                               8
3.26   4.04   4.53   4.89   5.17   5.40   5.60   5.77   5.92                               9
3.20   3.95   4.41   4.76   5.02   5.24   5.43   5.59   5.74                               10
3.15   3.88   4.33   4.65   4.91   5.12   5.30   5.46   5.60                               11
3.11   3.82   4.26   4.57   4.82   5.03   5.20   5.35   5.49                               12
3.08   3.77   4.20   4.51   4.75   4.95   5.12   5.27   5.39                               13
3.06   3.73   4.15   4.45   4.69   4.88   5.05   5.19   5.32                               14
3.03   3.70   4.11   4.41   4.64   4.83   4.99   5.13   5.25                               15
3.01   3.67   4.08   4.37   4.59   4.78   4.94   5.08   5.20                               16
3.00   3.65   4.05   4.33   4.56   4.74   4.90   5.03   5.15                               17
2.98   3.63   4.02   4.30   4.52   4.70   4.86   4.99   5.11                               18
2.97   3.61   4.00   4.28   4.49   4.67   4.82   4.96   5.07                               19
2.96   3.59   3.98   4.25   4.47   4.65   4.79   4.92   5.04                               20
2.95   3.58   3.96   4.23   4.45   4.62   4.77   4.90   5.01                               24
2.92   3.53   3.90   4.17   4.37   4.54   4.68   4.81   4.92                               30
2.89   3.49   3.85   4.10   4.30   4.46   4.60   4.72   4.82                              40
2.86   3.44   3.79   4.04   4.23   4.39   4.52   4.63   4.73                              60
2.83   3.40   3.74   3.98   4.16   4.31   4.44   4.55   4.65                            120
2.80   3.36   3.68   3.92   4.10   4.24   4.36   4.47   4.56                         Infinity
Degrees of Freedom Between
  1      2      3      4      5      6      7      8      9
5.70   6.98   7.80   8.42   8.91   9.32   9.67   9.97   10.24
5.24   6.33   7.03   7.56   7.97   8.32   8.61   8.87   9.10
4.95   5.92   6.54   7.01   7.37   7.68   7.94   8.17   8.37
4.75   5.64   6.20   6.62   6.96   7.24   7.47   7.68   7.86
4.60   5.43   5.96   6.35   6.66   6.91   7.13   7.33   7.49
4.48   5.27   5.77   6.14   6.43   6.67   6.87   7.05   7.21
4.39   5.15   5.62   5.97   6.25   6.48   6.67   6.84   6.99
4.32   5.05   5.50   5.84   6.10   6.32   6.51   6.67   6.81
4.26   4.96   5.40   5.73   5.98   6.19   6.37   6.53   6.67
4.21   4.89   5.32   5.63   5.88   6.08   6.26   6.41   6.54
4.17   4.84   5.25   5.56   5.80   5.99   6.16   6.31   6.44
4.13   4.79   5.19   5.49   5.72   5.92   6.08   6.22   6.35
4.10   4.74   5.14   5.43   5.66   5.85   6.01   6.15   6.27
4.07   4.70   5.09   5.38   5.60   5.79   5.94   6.08   6.20
4.05   4.67   5.05   5.33   5.55   5.73   5.89   6.02   6.14
4.02   4.64   5.02   5.29   5.51   5.69   5.84   5.97   6.09
3.96   4.55   4.91   5.17   5.37   5.54   5.69   5.81   5.92
3.89   4.45   4.80   5.05   5.24   5.40   5.54   5.65   5.76
3.82   4.37   4.70   4.93   5.11   5.26   5.39   5.50   5.60
3.76   4.28   4.59   4.82   4.99   5.13   5.25   5.36   5.45
3.70   4.20   4.50   4.71   4.87   5.01   5.12   5.21   5.30
3.64   4.12   4.40   4.60   4.76   4.88   4.99   5.08   5.16
Date      Version    Change
5/25/2012         67 in ws9 revert build data to sample mean 10.7 to match build tutorial

				
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