The variance of the mathematical scores of a sample of 21 high school girls was found to be 100 and that of a sample of 25 high school boys was 169.

Question

Test the hypothesis that the scores of the high school boys are more varying that those of the high school girls at alpha = 0.05.

Thanks!

Answer 1

This appears to be a hypothesis test involving inferences concerning two variances.

Sample 1 (Girls): n = 21; variance = 100; df = n - 1 = 20
Sample 2 (Boys): n = 25; variance = 169; df = n - 1 = 24

Test statistic = sample 1 variance / sample 2 variance

You can use the F-distribution at .05 level using the above information for degrees of freedom. This will be your critical value to compare to the test statistic. If the test statistic exceeds the critical value from the table, the null will be rejected in favor of the alternate hypothesis and you can conclude a difference in variances. If the test statistic does not exceed the critical value from the table, then the null is not rejected and you cannot conclude a difference.