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... 0 ng.cengage.com Dashboard Cengage O Ú Ú MindTap - Cengage Learning Suzanne Fendrick ? MINDTAP Chapter 11 Assignment . Due Today at 11:59 PM CDT Assignment: Chapter 11 Assignment Assignment Score: 83.21% Soave Submit Assignment for Grading Questions Exercise 1117 (Self-Test) Algorithmic « Question 6 of 14 > Check My Work eBook Video 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 $190 and a sample of 25 automobiles 2 years old showed a sample standard deviation for annual repair costs of $100. Let 4 year old automobiles be represented by population 1. a. State the null and alternative versions of the research hypothesis that the variance in annual repair costs is larger for the older automobiles. H, : o less than or equal to II. :o greater than b. Conduct the hypothesis test at a .01 level of significance. Calculate the value of the test statistic (to 2 decimals). O @ MK V VI O OG 2.89 8 The p-value is less than .01 . Use Table 11.1. What is your conclusion? Conclude that 4 year old automobiles have a larger variance in annual repair costs compared to 2 year old automobiles "Hide Feedback Partially CorrectExplanation / Answer
The statistical software output for this problem is:
Two sample variance summary hypothesis test:
12 : Variance of population 1
22 : Variance of population 2
12/22 : Ratio of two variances
H0 : 12/22 = 1
HA : 12/22 > 1
Hypothesis test results:
Ratio Num. DF Den. DF Sample Ratio F-Stat P-value
12/22 25 24 3.61 3.61 0.0012
Hence,
Test statistic = 3.61
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