A real estate agency says that the mean home sales price in Spring, Texas, is the same as in Austin, Texas. The mean home sales price for 25 homes in Spring is $127,414. Assume the population standard deviation is $25,875. The mean home sales price for 25 homes in Austin is $112,301. Assume the population standard deviation is $27,110. At α = 0.01, is there enough evidence to reject the agency’s claim?

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

(b) Find the critical value(s) and identify the rejection region(s),

(c) Find the standardized test statistic z,

(d) Decide whether to reject or fail to reject the null hypothesis,

(e) Interpret the decision in the context of the original claim. Assume the samples are random and independent, and the populations are normally distributed. If convenient, use technology.