It is believed that the SAT scores for students entering two state universities may have different standard deviations.Specifically,it is believed that the standard deviation at University A is greater than the standard deviation at University B.To test this using an alpha = 0.05 level,a sample of 14 student SAT scores from University A was selected and a sample of 8 SAT scores from University B was selected.The following sample results were observed: Based on this information,what is the value of the test statistic?
A)1.2407
B)0.6496
C)1.5394
D)None of the above.

Question

It is believed that the SAT scores for students entering two state universities may have different standard deviations.Specifically,it is believed that the standard deviation at University A is greater than the standard deviation at University B.To test this using an alpha = 0.05 level,a sample of 14 student SAT scores from University A was selected and a sample of 8 SAT scores from University B was selected.The following sample results were observed:  Based on this information,what is the value of the test statistic?
A)1.2407 
B)0.6496 
C)1.5394 
D)None of the above.

Quizplus · Accepted Answer

To test the hypothesis that the standard deviation of University A is greater than the standard deviation of University B, we can use the F-test. The test statistic for the F-test is calculated as the ratio of the variances of the two samples. In this case, we have:
Sample A: n1=14, variance s1^2 = 225.62
Sample B: n2=8, variance s2^2 = 50.50
The test statistic is therefore:
F = s1^2 / s2^2 = 225.62 / 50.50 = 4.472
The degrees of freedom for the F-test are (n1-1) and (n2-1), which are 13 and 7 in this case. Using a table of F-distributions or a calculator, we can find that the critical value of F at alpha=0.05 and degrees of freedom 13 and 7 is 3.046. Since our calculated F-value of 4.472 is greater than the critical value of 3.046, we reject the null hypothesis and conclude that the standard deviation of University A is indeed greater than the standard deviation of University B.

It Is Believed That the SAT Scores for Students Entering