Question

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 $180 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

H_a: σ₁² = σ₂²

H₀: σ₁² > σ₂²

H_a: σ₁² ≤ σ₂²

    

H₀: σ₁² ≤ σ₂²

H_a: σ₁² > σ₂²

H₀: σ₁² = σ₂²

H_a: σ₁² ≠ σ₂²

(b)

At a 0.01 level of significance, what is your conclusion?

Find the value of the test statistic.

test statistic=

Find the p-value. (Round your answer to four decimal places.)

p-value =

State your conclusion.

a)Reject H₀. We cannot conclude that 4-year-old automobiles have a larger variance in annual repair costs compared to 2-year-old automobiles.

b)Reject H₀. We can conclude that 4-year-old automobiles have a larger variance in annual repair costs compared to 2-year-old automobiles.     

c)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.

d)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.

Discuss the reasonableness of your findings.

This is expected due to the fact that  ---Select--- (younger /older) automobiles are more likely to have some more expensive repairs which lead to greater variance in the annual repair costs.

Answer 1