In its 2016 Auto Reliability Survey, Consumer Reports asked subscribers to report their maintenance and repair costs. 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 $210 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.
H0: σ12 = σ22 Ha: σ12 ≠ σ22
H0: σ12 ≠ σ22 Ha: σ12 = σ22
H0: σ12 > σ22 Ha: σ12 ≤ σ22
H0: σ12 ≤ σ22 Ha: σ12 > σ22
(b) At a 0.01 level of significance, what is your conclusion? Find the value of the test statistic.
test stat =
(c) Find the p-value. (Round your answer to four decimal places.)
p-value =
(d) State your conclusion.
i. Reject H0. We can conclude that 4-year-old automobiles have a larger variance in annual repair costs compared to 2-year-old automobiles.
ii. Reject H0. We cannot conclude that 4-year-old automobiles have a larger variance in annual repair costs compared to 2-year-old automobiles.
iii. Do not reject H0. We cannot conclude that 4-year-old automobiles have a larger variance in annual repair costs compared to 2-year-old automobiles.
iv. Do not reject H0. We can conclude that 4-year-old automobiles have a larger variance in annual repair costs compared to 2-year-old automobiles.