Question

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 $140 and a sample of 23 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. H60, greater than H0 : less than or equal to b. Conduct the hypothesis test at a .01 level of significance. Calculate the value of the test statistic (to 2 decimals). 2.89 The p-value is less than 01 What is your conclusion? Do not conclude that 4 year old automobiles have a larger variance in annual repair costs compared to 2 year old automobiles

Answer 1

Step1:To, test the two population variances are same at the 5% level of significance Assumptions: 1. The samples are simple random samples. 2. The two samples are independent and are approximately normally distributed Utilize the F-distribution to test for the variances, Sample 1: n = 26, sample variance s = 19600. Sample 2: Y = 23, sample variance s = 10000. The null and alternative hypotheses: H.: 0 = 0 versus H: > Step2: The level of significance is a =0.01. (b) Step3: The formula for calculating the F-test statistic is - = 19600 10000 = 1.96 F, 1.96 Therefore, the value of the F-test statistic is F, 1.96 Step 4: If the test statistic is F > F-0014: -25, -2 = 2.732764. We reject the null hypothesis H. Otherwise, we do not reject the null hypothesis H. The P-value approach: P-value = P(F>) = 1-P(F<F) 1-P(F <1.96) 1-0.942496 0.057504 P-value > 0.057504 > a = 0.01). We do not reject the null hypothesis Ho Step 5: Conclusion: Since, the test statistic is F = 1.96 <F_00L-25.8.-22 = 2.732764 We do not reject the null hypothesis Ho Since, the probability value is P-value > 0.0575 > a= 0.01 We do not reject the null hypothesis H. The data do not provide sufficient evidence to conclude that the variance in annual repair costs of 4 year old automobiles is larger than that of the annual repair costs of 2 year old automobiles at the 1% level of significance.