Question

Use Table H in the Appendix for this problem. A researcher hypothesized that the variation in the car rental rates (in US$/day) at a major city airport is less than in the car rental rates down town. A survey found that the variance of the rental rates on 8 cars at the airport was 35.7 while the variance of the rental rates on 5 cars down town was 50.4. At the 0.01 level of significance, is there sufficient evidence to support the claim that car rental rates at the airport are less than down town?

Evaluate using a Traditional Hypothesis Test.

Hypothesis with claim: Draw the curve, labeling the

CV, TV, and shading the critical region.

  

dfN =  

dfD =   

CV(s):

TV:

Decision:

Summary:

Answer 1

The formula of F-test statistic for testing the equality of variances as follow.

Where is the sample variance of group with largest variance.

and Where is the sample variance of group with smallest variance.

dfN = numerator degrees of freedom = 5 - 1 = 4

dfD = denominator degrees of freedom = 8 - 1 = 7

Let's use minitab for shading the critical region.

For one tailed F test of equality of variances, we need to put 2* = 2 * 0.01 = 0.02

From the above graph the CV(s) = 6.035

Let's find test statistic value TV

So that TV = 1.412

Decision : Since TV = 1.412 < CV = 6.035 we fial to reject the null hypothesis and conclude that there was not sufficient evidence to support the claim that car rental rates at the airport are less than down townat 1% level of significance.