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General Statistics
Chapter 8
Definition of Key Terms
Inference: Two Samples Means and Proportions
Two Sample Statistics Testing (two populations means)

The hypothesis testing involving two different means study the distribution of their differences:.
 
For large sample size () the test statistics in a hypothesis test is:

, the z-score

 For small sample size () the test statistics in a hypothesis test is:

, the student's t, df = n-1

For large sample size the standard deviation and test statistics are:
 
Standard Deviation:

Also 

 Test statistics, z

For small sample size the standard deviation and test statistics are:
 
Standard Deviation:

Pooled sample standard deviation when

Also 

 Test statistics, t, df = n-1 (smallest sample size)

Pooled Test statistics, t ,  when 

Confidence Interval is 

Pooled t-test

If samples being compared are from the same population where , then the simplified pooled statistics can be used to evaluate the test of two samples means.
 
Pooled Test statistics, t ,  when 

Confidence Interval is 

 Pooled Standard deviation

Two Sample Statistics Testing (two population proportions)
 
Estimates of sample proportions, p1 and p2 are:

and 

The pooled data proportion is:

and 

Estimate of combined proportion standard deviation is:

The test statistics is:

, where 

The difference of both proportion mean is:

(assume population proportions are the same)

Standard deviation:

Confidence Interval for  is:

Decision rules:

Upper-Tailed Test ():

Accept H0 if 

Reject H0 if 

Lower-Tailed Test ():

Accept H0 if 

Reject H0 if 

Two-Tailed Test ():

Accept H0 if 

Reject H0 if