Question

Most individuals are aware of the fact that the average annual repair cost for an automobile depends on the age of the automobille. 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 160 and a sample of 24 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 varlance in annual repair costs is larger for the clder automobiles. H o: σ s 21 less than or equal to H .: ơ 1 , greater than σ 2 2 v b. Conduct the hypothesis test at a.01 level of significance Calculate the value of the test statistic (to 2 decimals).

Answer 1

b)

here as we know that test statistic F =(s1/s2)² =(160/100)² =2.56

(for 0.01 level and (n1-1=25) ; (n2-1=23) degree of freedom crtical value =2.69)

as test statistic 2.56 is not higher then critical value ; we fail to reject null hypothesis

we can not conclude that variance in annual repair cost is larger for older automobiles