Question

In: Statistics and Probability

In 2003, Major League Baseball took steps to speed up the paly of baseball games and...

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)

Solutions

Expert Solution

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​​​​​​22 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.


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