A real estate agency says that the mean home sales price in Olathe, Kansas, is greater than in Rolla, Missouri. The mean home sales price for 64 homes in Olathe is $356,889. Assume the population standard deviation is $537,407. The mean home sales price for 36 homes in Rolla is $189,389. Assume the population standard deviation is $113,555. At α = 0.05, is there enough evidence to support the agency’s claim?

For each exercise, perform the steps below.

(a) Identify the claim and state H₀ and H_a.

(b) Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed, and whether to use a z-test or a t-test. Explain your reasoning.

(c) Find the critical value(s) and identify the rejection region(s).

(d) Find the appropriate standardized test statistic.

(e) Decide whether to reject or fail to reject the null hypothesis.

(f) Interpret the decision in the context of the original claim.