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 $171.61 and a sample of 23 automobiles 2 years old showed a sample standard deviation for annual repair costs of $118.74. Let 4 year old automobiles be represented by population 1. The data is located in the Microsoft Excel Online file below.

Open spreadsheet

State the null and alternative versions of the research hypothesis that the variance in annual repair costs is larger for the older automobiles.

H₀: ²₁

less than or equal to ²₂

H_a: ²₁ greater than ²₂

Conduct the hypothesis test at a 0.10 level of significance.

Calculate the value of the test statistic (2 decimals).

Calculate the critical value (2 decimals).

Calculate the p-value (4 decimals).

Car Age and Repair Cost ($)
4 years	2 years
777	638
839	431
778	454
791	404
893	405
791	713
775	573
943	469
1013	155
949	435
1060	399
405	524
955	396
874	548
890	397
336	598
733	391
654	336
507	370
823	455
708	356
808	365
898	569
790
801
612