Question

A real estate agency says that the mean home sales price in City A is the same as in City B. The mean home sales price for 30 homes in City A is $127,466. Assume the population standard deviation is $25,877. The mean home sales price for 30 homes in City B is $112,349. Assume the population standard deviation is $27,108. At alpha=0.01, is there enough evidence to reject the agency's claim? Complete parts (a) through (d) below.

(a) Identify the claim and state H₀ and ₁Ha. What is the claim?
A. The mean home sales price in City A is greater than as in City B.
B. The mean home sales price in City A is less than in City B.
C. The mean home sales price in City A is the same as in City B.
D. The mean home sales price in City A is not the same as in City B.

Answer 1

The claim by the real estate agency is that the mean home sales price in City A is the same as in City B. The null hypothesis is H0: μA = μB, and the alternative hypothesis is Ha: μA ≠ μB. A two-sample z-test at alpha = 0.01 is used to test the hypothesis.

Step-by-step explanation:

To determine if there is enough evidence to reject the real estate agency's claim that the mean home sales price in City A is the same as in City B at an alpha level of 0.01, we must first identify the claim and state the null hypothesis (H0) and the alternative hypothesis (Ha).

The claim made by the agency corresponds to option C: The mean home sales price in City A is the same as in City B. Based on this claim, the null hypothesis would be H0: μA = μB, where μA is the mean sales price in City A and μB is the mean sales price in City B. The alternative hypothesis, which represents the opposite of the claim, would be Ha: μA ≠ μB, indicating the means are not equal.

To test the hypothesis, we would perform a two-sample z-test since the population standard deviations are known. If the calculated p-value from the test is less than the significance level of 0.01, we have enough evidence to reject the null hypothesis in favor of the alternative.