# Extra Notes

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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:

.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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