A car salesman claims that the variance of prices on convertibles is higher than the variance on station wagons.The standard deviation of 16 convertibles is $6,800 and the standard deviation of 24 station
Wagons is $3,900.For α = 0.05, what is the test value?
A)3.00
B)3.04
C)2.78
D)2.33

Question

Quizplus · Accepted Answer

To test the salesman's claim, we use the F-test for two variances. 
The null hypothesis is that the variances are equal, and the alternative hypothesis is that the variance of prices on convertibles is higher than the variance on station wagons.

F = (s_1^2 / s_2^2) = (6,800^2 / 3,900^2) = 4.04

Using a calculator or a F-distribution table with (df_1 = 16-1 = 15, df_2 = 24-1 = 23) and α = 0.05, we find that the critical value is 2.78.

Since our test value (F = 4.04) is greater than the critical value (2.78), we reject the null hypothesis and conclude that the variance of prices on convertibles is indeed higher than the variance on station wagons.

The closest answer choice is B) 3.04, which is the test value rounded to two decimal places.

A Car Salesman Claims That the Variance of Prices on Convertibles