Question

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 $171.07 and a sample of 23 automobiles 2 years old showed a sample standard deviation for annual repair costs of $118.52. Let 4 year old automobiles be represented by population 1. The data is located in the Microsoft Excel Online file below. Car Age and Repair Cost ($)

Car Age and Repair Cost ($)
4 years	2 years
788	630
839	431
778	454
791	404
884	391
791	713
775	573
943	469
1013	155
938	436
1060	399
405	524
955	396
874	548
894	394
336	598
733	391
654	336
507	370
823	455
708	356
808	365
898	569
790
801
612

Answer 1

F-test ratio of variance

using Excel

data -> data analysis ->

F-Test Two-Sample for Variances
	4 years	2 years
Mean	784.5384615	450.3043478
Variance	29266.25846	14046.03953
Observations	26	23
df	25	22
F	2.083595052
P(F<=f) one-tail	0.043066491
F Critical one-tail	2.019644344

p-value = 0.0431

p-value < 0.05

hence we reject the null hypothesis

we conclude that there is evidence that

the variance of the annual repair costs also increases with the age of the automobile.