Question

suppose the null hypothesis is not rejected. state the conclusion based on the results of the test. three years ago, the mean price of a single - family home was $243,761. a real estate broker believes that the mean price has decreased since then. which of the following is the correct conclusion? o a. there is sufficient evidence to conclude that the mean price of a single - family home has decreased. o b. there is not sufficient evidence to conclude that the mean price of a single - family home has not changed. o c. there is not sufficient evidence to conclude that the mean price of a single - family home has decreased. o d. there is sufficient evidence to conclude that the mean price of a single - family home has not changed.

Explanation:

Step1: Understand hypothesis testing

In hypothesis testing, when the null hypothesis ($H_0$) is not rejected, we fail to support the alternative hypothesis ($H_1$). Here, $H_0:\mu = 243761$ (no change in mean price from the initial value) and $H_1:\mu<243761$ (mean price has decreased).

Step2: Analyze the conclusion

Since the null hypothesis is not rejected, we cannot say that the mean price has decreased (which is what the alternative hypothesis claims). We do not have enough evidence (from the non - rejection of the null) to support the claim of a decrease. Options A and D suggest sufficient evidence for a claim (either decrease or no change) which is wrong as we failed to reject the null. Option B is about no change, but our alternative is about a decrease. So, we conclude that there is not sufficient evidence to conclude that the mean price of a single - family home has decreased.

Answer:

C. There is not sufficient evidence to conclude that the mean price of a single - family home has decreased.