A small business owner has two fast food restaurants. The owner wants to determine if there is any difference in the variability of service times at the drive-thru window of each restaurant. A sample of size n = 9 is taken from each restaurant's drive-thru window. To perform a hypothesis test using the 0.05 level of significance the critical value is:
A) 3.438
B) 3.197
C) 4.026
D) 4.433

Question

Quizplus · Accepted Answer

The critical value for testing the difference in variability (variance) between two samples can be found using the F-distribution table. Given the level of significance (alpha) is 0.05 and the sample size for both samples is n = 9 (which gives us degrees of freedom df1 = df2 = 8 for both samples), the critical value for a two-tailed test is found at the intersection of the appropriate degrees of freedom. Since the question does not specify the direction of the test (whether one variance is greater than the other or vice versa), we assume a two-tailed test. The critical value for F with df1 = df2 = 8 at the 0.05 level of significance for a two-tailed test is typically found in the upper tail, and for such cases, tables or software might be needed to find the exact value. The provided options suggest a specific value, and among them, 4.433 is a plausible critical value for an F-test in this context, considering it might be the value for either the upper or lower critical value depending on the table or software used.

A Small Business Owner Has Two Fast Food Restaurants