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 $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.

Answer 1

Explanation:

A.

Null hypothesis

H0: σ1² ≤ σ2²

Alternative hypothesis

H1: σ1² > σ2²

We have level of significance = 0.01

Test statistic

F = S1²/S2²

= 170²/100²

= 28900/10000

F = 2.89

Df = degrees of freedom

Df1 = n1 - 1

= 26-1

= 25

Df2 = n2 - 1

= 25-1

= 24

B. We get the p value using f distribution

Fdist(2.89,25,24)

P value = 0.0057

The p-value is less than 0.01 so we reject null hypothesis.

So we conclude that automobiles that are of 4 years have their variances to be larger In annual repair costs than those that are of 2 years.

Reasonableness: we expect this since 4byears old automobiles are more likely to have more expenses during repair leading to greater variances

Answer 2

Explanation:

A.

Null hypothesis

H0: σ1² ≤ σ2²

Alternative hypothesis

H1: σ1² > σ2²

We have level of significance = 0.01

Test statistic

F = S1²/S2²

= 170²/100²

= 28900/10000

F = 2.89

Df = degrees of freedom

Df1 = n1 - 1

= 26-1

= 25

Df2 = n2 - 1

= 25-1

= 24

B. We get the p value using f distribution

Fdist(2.89,25,24)

P value = 0.0057

The p-value is less than 0.01 so we reject null hypothesis.

So we conclude that automobiles that are of 4 years have their variances to be larger In annual repair costs than those that are of 2 years.

Reasonableness: we expect this since 4byears old automobiles are more likely to have more expenses during repair leading to greater variances