Question

The homework question states:

With gasoline prices increasing, drivers are more concerned with their cars' gasoline consumption. For the past 5 years, a driver has tracked the gas mileage of his car and found that the variance from fill up to fill up was 23mpg. Now that his car is 5 years old, he would like to know whether the variability of gas mileage has changed. He recorded the mileage from his last 8 fill ups. Conduct a test at a 10% significant level to infer whether the variability has changed.

28 25 29 25 32 36 27 24.

My question is that I found s² to be 16.5 and x² to be 5.02,but using the table in the appendix, how do I set up the rejection region? Our class does not use Excel

Answer 1

From the given sample data : n=8 , ,

The sample variance is ,

Hypothesis : VS  

The test statistic is ,

The critical values are given by from table,

The rejection region is (0,2.167) and (14.057,)

Decision : Here , the value of the test statistic does not lies in the rejection region.

Therefore , do not reject Ho

Conclusion : Hence , there is not sufficient evidence to support the claim that the variability of gas mileage has changed.