Question

In 2003, Major League Baseball took steps to speed up the paly of baseball games and make games a more consistent duration. In a sample of 41 games in 2002, the average duration of a game was 2 hours and 58 minutes with a standard deviation of 32 minutes. A similar survey in 2003 of 31 games found that the average duration was 2 hours and 40 minutes with a standard deviation of 19 minutes. When testing the hypothesis (at the 10% level of significance) that the variance has been reduced, what is the critical value? (please round your answer to 2 decimal places)

Answer 1

Solution:

The null and alternative hypotheses will be as follows:

To test the equality of two population variances, the most appropriate test is F-test. The test statistic is given as follows:

Where, S_{​​​​​​1}^{​​​​​2} and S_{​​​​​​2}² are sample variances.

The degrees of freedom for the test will be (n_{​​​​​​1} - 1, n_{​​​​​​2} - 1). Where, n_{​​​​​​1} and n_{​​​​​​2} are sample sizes.

Since, our test is right-tailed test, therefore we shall obtain right-tailed critical value. The right-tailed critical value for F-test is given by,

Where, α is significance level, and (n_{​​​​​​1} -1, n_{​​​​​​2} - 1) is degrees of freedom.

We have,  α = 10% = 0.10,  n_{​​​​​​1} = 41 and n_{​​​​​​2} = 31

Using F-table we get,

The critical value is 1.57.