# student_worksheets

Document Sample

```					                                                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
37                                                8
38                                               13
39                                               10
40                                               16
41                                               15
42                                               12
43                                               16
44
45                                 5
46                                 6
47                                 7
48                                 5
49                                 3
50                                 8
51                                 7
52                                 2
53                                 1
54                                 5
55
56
57
58
59
60
61
62
63
64
65
66
67
68

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
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92

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

K    L        M      N    O      P
1 6▼ 7▼          8 ▼ 14 ▼   15 ▼
2     DeviationSquared Std z-score
3 Mean Score Dev Sc Dev      Z=
2
4  x X - x (X - x) S (X - x) / S
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34

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

K   L   M   N   O   P
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68

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

K   L   M   N   O   P
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92

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
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
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
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

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%
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
10
9
8
7
6
5
4
3
2
1
5
4
6
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 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

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
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
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
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

```
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
 views: 36 posted: 9/13/2012 language: Unknown pages: 103