It is believed that the SAT scores for students entering two state universities

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 significance level alpha = 0.05, a sample of 14 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:

Question data: Final_Q15.xlsx

Based on this information, what is the critical value that will be used to test the hypothesis?

Question 15 options:

F = 3.55

F = 2.832

z = 1.645

F = 3.237

University A University B Sample mean 1104 1254 Sample Standard Deviation 134 108 Sample size 14 8

Explanation / Answer

We will use f-test for test of equality of two variances.

Level of significance = 0.05 and this a one-sided test

µA = 1104; A = 134; NA = 14

µB = 1254; B = 108; NB = 8

We can find out the critical value looking at the f-test table or using excel.

For numerator degrees of freedom = 13 and denominator degrees of freedom = 7

Critical value, F = 3.55

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