Final answer:
To determine if there is enough evidence to reject the real estate agency's claim that the mean home sales price is the same in City A and City B, a two-sample z-test is used. If the p-value is less than α = 0.01, the null hypothesis is rejected, suggesting the means are not equal.
Step-by-step explanation:
The real estate agency's claim is that the mean home sales price in City A is the same as in City B. Statistically, this is represented as the null hypothesis, which we are testing against the alternative hypothesis that the means are not equal. To test this claim, we use a two-sample z-test for the difference between two means because the sample sizes are less than 30 and the population standard deviations are known.
Given that the sample means and population standard deviations are provided for both cities, and with a significance level (α) of 0.01, we calculate the z-test statistic which informs us whether the observed difference between the sample means is statistically significant.
If the calculated p-value from the z-test statistic is less than the significance level, we reject the null hypothesis. In this context, rejecting the null hypothesis would mean that we have enough evidence to reject the agency's claim that the means are equal (Option C) and support the claim that they are not equal (Option D). However, we cannot say whether the mean home sales price in City A is greater than (Option A) or less than (Option B) in City B without additional information such as the direction of the z-test (one-tailed or two-tailed).