General Statistics
Statistical Inference
Summary of Statistical Hypothesis testing

Summary of Statistical Hypothesis testing for Chapter 8.  - click on images to see larger pictures

Hypothesis Testing: Comparing the means of two samples with each other. Question: Is  ?
 
We Wish to Test Whether Assumptions

Confidence Interval

Test Statistics Accept H0 if

( p-value: )

H

H0

sample size large (), and  known

Example



 

Reference Table

or 

 

H

H0

sample size small (), and  is unknown

Estimate  from s

(smallest of the two)

Example


Reference Table

H

H0

sample size large (), and  known

Example


Reference Table

H

H0

sample size small (), and  is unknown

Estimate  from s

(smallest of the two)

Example


Reference Table

H

H0

sample size large (), and  known

Example


Reference Table

H

H0

sample size small (), and  is unknown

Estimate  from s

(smallest of the two)

Example


Reference Table

 

Pooled T-test
H

H0

sample size small (), and  is unknown

Estimate  from s

(smallest of the two)

Example

Pooled t-test

Reference Table

See test Above

 

Hypothesis Testing: Comparing the two sample proportions with each other.
 
We Wish to Test Whether Assumptions

Confidence Interval

Test Statistics Accept H0 if

( p-value: )

 : 
Two-Tailed Test

Accept H0 if 

Reject H0 if 

sample size large

 ()

Estimate 

Example


The test statistics is:

, where 

Reference Table

or 

 

 :
Upper-Tailed Test

Accept H0 if 

Reject H0 if 

sample size large

()

Estimate 

Example


The test statistics is:

, where 

Reference Table


Lower-Tailed Test

Accept H0 if 

Reject H0 if 

sample size large

()

Estimate 

Example


The test statistics is:

, where 

Reference Table