A researcher hypothesizes that the variation in the car rental rates at a major citiy's airport is less than the car rental rates in that city. The variance of 7 airport car rental rates was $25 and the variance of 4 city car
Rental rates was $60. What is the test value?
A) 4.20
B) 1.55
C) 2.40
D) 5.76

Question

Quizplus · Accepted Answer

To test the hypothesis, we can use the F-test for comparing variances. The test value is calculated as the ratio of the sample variances:
F = variance of airport rates / variance of city rates = 25/60 = 0.4167
Now we need to compare this value to the critical F-value for our degrees of freedom. Since we have 7 airport rates and 4 city rates, the degrees of freedom are (7-1) = 6 and (4-1) = 3, respectively. Using a significance level of 0.05, the critical F-value for these degrees of freedom is 4.26. Since our test value is less than the critical value, we fail to reject the null hypothesis that the variance of airport rates is less than or equal to the variance of city rates. Therefore, we can conclude that the variation in the car rental rates at the airport is less than the car rental rates in the city. The closest option is C) 2.40, which is a rounded value of the calculated F-value.

A Researcher Hypothesizes That the Variation in the Car Rental