Based on a random sample of 13 tire changes, the mean time to change a tire on a Boeing 777 has a mean of 59.5 minutes with a standard deviation of 8.4 minutes. For 10 tire changes on a Boeing 787, the mean time was 64.3 minutes with a standard deviation of 12.4 minutes. To test for equal variances in a two-tailed test at α = .10, the critical values are:
A)3.73 and 0.228
B)2.51 and 3.67
C)3.07 and 0.398
D)3.07 and 0.357

Question

Quizplus · Accepted Answer

We can use the F-distribution to test for equal variances. The formula for the F-test is:

F = s1^2 / s2^2

where s1 and s2 are the sample standard deviations and the F-distribution has n1-1 and n2-1 degrees of freedom (in this case, n1=13 and n2=10).

The critical values for a two-tailed test at α = .10 with 12 and 9 degrees of freedom are 3.07 and 0.357.

The calculated F-value is:

F = 8.4^2 / 12.4^2 = 0.456

Since 0.357 < 0.456 < 3.07, we fail to reject the null hypothesis and conclude that there is no significant difference in variances between the two groups. Therefore, the best choice is D.

Based on a Random Sample of 13 Tire Changes, the Mean