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 $\alpha$ = .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

To test for equal variances, we need to calculate the F-statistic which is the ratio of the sample variances. Using the formula:

F = (s1)^2 / (s2)^2

where s1 is the variance of the first sample and s2 is the variance of the second sample.

For our problem, we have:

s1^2 = 8.4^2 = 70.56
s2^2 = 12.4^2 = 153.76

So,

F = 70.56 / 153.76 = 0.458

To find the critical values, we need to look up the F-distribution table with degrees of freedom (df) of 12 and 9 (n1-1 and n2-1). At alpha level of 0.10, the critical values are 0.357 and 3.07. Therefore, the answer is D.

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

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