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					Extra Notes
   Dr. Ahmad Syamil
   QM 2113 Business Statistics
     Chapter 2
     Mutually exclusive classes
Age:

1)   Less than 10 years
2)   10 – less than 25
3)   25 – less than 30
4)   30 and over
                 Chapters 4 and 5




For any types of distribution (normal, uniform, binomial,
exponential, Poisson, etc.):

Standard deviation = SQRT (variance)
Chapter 4
   Elementary events:

.e1=head
.e2=tail

Sample space: {e1,e2}
Chapter 4
Probability Assessments
   Classical (a priory)
   Relative frequency
   Subjective
Data/distribution/variable
 Discrete ->counting process  Chapter
  5
Population, # of chairs
100,000; 5 chairs, etc. -> integer
 Continuous  Measurement process -

  Chapter 5
Height, weight, distance, etc.
1.25; 8.768; 12.876 ->fraction is OK
       Chapter 5
       Discrete dist.


   Uniform
   Binomial
   Poisson
   Others
Chapter 6
Continuous Dist.
   Normal/bell curve/ z distribution
   Uniform
   Exponential
   Others:
    o   Student’s t distribution (Chapter 7)
    o   Chi-square distribution (Chapter 8)
  Chapter 5


2 Types of Normal Distribution Problems:
•  Given Z or calculate Z and then find P (=big
   “P” =percentage =probability =chance)
•  Given P, then find X,  or 
You solve them using:
                     and normal/z distribution
            x
       z
             
Poisson & Exponential Dist
 Waiting line:
Banks , McDonald, Wal-Mart:
o Number of customers/hour  discrete

  (Poisson/Chapter 5)
o Mean time between customer ->
  continuous (Exponential/Chapter 5)
Chapter 6: Sampling
Distribution
 Mean
 Proportion

 We solve them using Z (normal)
  distribution
        Chapter 7 Summary
1.      Point Estimate
     1.     x (sample mean)   (population mean)
     2.     .p (sample proportion)   (population proportion)
2.      Confidence Interval
     1.     Population mean ()
           a.    (population standard deviation) is given (known):
                  Use z (standard normal distribution)
           b.    (pop std dev) is not given but s (sample std dev) is given
                 Use student’s t distribution
     2.     Population proportion ()  Use z (standard normal distribution)
     Note: p = “small p” = sample proportion
              P = “big P” = probability = chance
    Chapter 7
SAMPLE PROPORTION


                   x
               p 
                   n
Where:


          p = Sample proportion
          x = Number of items in the
sample having the attribute
          n = sample size
Chapter 7
CNN/Gallup Pool/USA Today
   The margin of error is the sampling
    error if the level of confidence = 95%

Bush = 51%  [48%, 54%]
Gore = 49% -> [46%, 52%]
Margin of error = 3%
Chapter 7
Student’s t distribution


Degrees of freedom = sample size –
 number of parameters

. df = n – k
Chapter 7 ->        k = 1 (always)
 Therefore, in Chapter 7, df = n -1
                  Chapter 13
    Summary: Simple Linear Regression Analysis
                Page 528, Step 5

(a)t test for b1 (regression slope) = Fig.
  13-18, page 528.
(b).t test for  (rho = coefficient of
  correlation) = Fig. 13-6, page 508.
(c  extra) F test for testing the overall
  regression model (equation)
All of the 3 tests MUST produce the same
  conclusion.

				
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