Tri-State Mazda is a Mazda dealership in eastern Pennsylvania. They recently sta

Question

Tri-State Mazda is a Mazda dealership in eastern Pennsylvania. They recently stated in an advertisement that Mazda owners averaged at least 90,000 miles before trading in or selling their Mazda cars. To test this, an independent agency selected a simple random sample of 25 Mazda owners who have either traded or sold their Mazda and determined the number of miles on the cars when the owner parted with them. They plan to test Tri-Stat’s claim at the 5% level of significance.

a.) Suppose the sample of n = 25 Mazda owners provides a sample mean of X = 85,000 miles and a sample standard deviation of S =10,000 miles. Conduct a formal test of hypothesis to determine what conclusion should be reached about the claim? Interpret the results. Set up a left-tailed test, the decision rule and your decision.

b.)Use Excel to find the p-value for the test. Do you reach the same decision you reached in part b? Explain. What does the p-value measure?

Explanation / Answer

Below are the null and alternate hypothesis
H0: mu = 90000
H1: mu < 90000

Test statistics, t = (85000 - 90000)/(10000/sqrt(25)) = -2.5

p-value = 0.0062 (Excel Formula used: =NORM.DIST(-2.5,0,1,TRUE))

As p-value is less than significance level of 0.05, we reject the null hypothesis.

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