Tests for Variances

In each case, we'll illustrate how to perform the hypothesis tests of this lesson using summarized data.

Hypothesis Test for One Variance

(1) Under the Stat menu, select Basic Statistics, and then select 1 Variance...:

(2) In the pop-up window that appears, in the box labeled Data, select Sample standard deviation (or alternatively Sample variance). In the box labeledSample size, type in the size n of the sample. In the box labeled Sample standard deviation, type in the sample standard deviation. Click on the box labeled Perform hypothesis test, and in the box labeled Value, type in theHypothesized standard deviation (or alternatively the Hypothesized variance): 

(3) Click on the button labeled Options... In the pop-up window that appears, for the box labeled Alternative, select either less than, greater than, or not equal depending on the direction of the alternative hypothesis:

Then, click on OK to return to the main pop-up window.

(4) Then, upon clicking OK on the main pop-up window, the output should appear in the Session window: 

 

Hypothesis Test for Two Variances

(1) Under the Stat menu, select Basic Statistics, and then select 2 Variances...:

(2) In the pop-up window that appears, in the box labeled Data, select Sample standard deviations (or alternatively Sample variances). In the box labeled Sample size, type in the size n of the First sample and m of theSecond sample. In the box labeled Standard deviation, type in the sample standard deviations for the First and Second samples: 

(3) Click on the button labeled Options... In the pop-up window that appears, in the box labeled Value, type in the Hypothesized ratio of the standard deviations (or the Hypothesized ratio of the variances). For the box labeled Alternative, select either less than, greater than, or not equal depending on the direction of the alternative hypothesis:

Then, click on OK to return to the main pop-up window.

(4) Then, upon clicking OK on the main pop-up window, the output should appear in the Session window: