Most individuals are aware of the fact that the average annual repair cost for an automobile depends on the age of the automobile. A researcher is interested in finding out whether the variance of the annual repair costs also increases with the age of the automobile. A sample of 26 automobiles 4 years old showed a sample standard deviation for annual repair costs of $170 and a sample of 25 automobiles 2 years old showed a sample standard deviation for annual repair costs of $100.
a. State the null and alternative versions of the research hypothesis that the variance in annual repair costs is larger for the older automobiles.
b. At a .01 level of significance, what is your conclusion? What is the p-value? Discuss the reasonableness of your findings.