12.3 - Using Minitab

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

Hypothesis Test for One Variance Section

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

    minitab

  2. In the pop-up window that appears, in the box labeled Data, select Sample standard deviation (or alternatively Sample variance). In the box labeled Sample 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 the Hypothesized standard deviation (or alternatively the Hypothesized variance):

    minitab

  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:

    minitab

    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:

    95% Confidence Intervals
    Method CI for
    StDev    		 CI for
    Variance
    Chi-Square (39.7,  62.3) (1578,  3878)
    Tests
    Method Test
    Statistic    		 DF P-Value
    Chi-Square 57.34 39 0.059

     

Hypothesis Test for Two Variances Section

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

    minitab

  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 the Second sample. In the box labeled Standard deviation, type in the sample standard deviations for the First and Second samples:

    minitab

  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:

    minitab

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

    1. Then, upon clicking OK on the main pop-up window, the output should appear in the Session window:

      Test and CI for Two Variances

      Method

      Null hypothesis                 Sigma(1)  /  Sigma(2)  = 1
      Alternative hypothesis     Sigma(1)  /  Sigma(2)  not  = 1
      Significance level              Alpha  =  0.05


      Statistics

      Sample N StDev Variance
      1 29 12.200 148.840
      2 34 20.100 404.010

      Ratio of standard deviations  =  0.607
      Ratio of variances  =  0.368


      95% Confidence Intervals 

      Distribution
      of Data      		 CI for StDev Ratio CI for
      Variance Ratio
      Normal (0.425,  0.877) (0.180,  0.770)
      Tests
      Method DF1 DF2 Test
      Statistic      		 P-Value
      F Test (normal) 28 33 0.37 0.009