Null Hypotheses

9.32

Previous experience shows the variance of a given process to be 14. Researchers are testing to determine whether this value has changed. They gather the following dozen measurements of the process. Use these data and α = .05 to test the null hypothesis about the variance. Assume the measurements are normally distributed.

 

52

44

51

58

48

49

38

49

50

42

55

51

 

 n = 12

 α = .05

σ2 = 14

 s2 = ?

 

 

Step #1: Hypothesize.

H0: σ2 = 14

Ha: σ2 ≠ 14

This is a two-tailed test.

 

Step #2: Test.

Data is assumed to be normally distributed.

 

Step #3:

α = .05, α/2 = .025

 

Step #4:

df = n -1

df = 12 -1 = 11

The two critical chi-square values are:  and

From Table A.8:

           

 

 

Now calculate the chi-square value. IF the calculated (observed) chi-square value is:

 

            3.81574 <  < 21.9200

 

we will FAIL to reject the null hypothesis.

 

Step #6:

From excel calculations:

 

s2 = 30.08

 

The observed chi-square value is calculated as:

 

 

 

Step #7: Action.

This observed chi-square value is in the Rejection Region because:

 

The company REJECTS the null hypothesis.

 

The results indication, with 95% confidence, that the variance is not 14.