Questions: 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 243,784. A real estate broker believes that the mean price has decreased since then. Which of the following is the correct conclusion? A. There is not sufficient evidence to conclude that the mean price of a single-family home has not changed. B. There is sufficient evidence to conclude that the mean price of a single-family home has not changed. C. There is sufficient evidence to conclude that the mean price of a single-family home has decreased. D. There is not sufficient evidence to conclude that the mean price of a single-family home has decreased.

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 243,784. A real estate broker believes that the mean price has decreased since then.

Which of the following is the correct conclusion? A. There is not sufficient evidence to conclude that the mean price of a single-family home has not changed. B. There is sufficient evidence to conclude that the mean price of a single-family home has not changed. C. There is sufficient evidence to conclude that the mean price of a single-family home has decreased. D. There is not sufficient evidence to conclude that the mean price of a single-family home has decreased.

Transcript text: 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 $\$ 243,784$. A real estate broker believes that the mean price has decreased since then. Which of the following is the correct conclusion? A. There is not sufficient evidence to conclude that the mean price of a single-family home has not changed. B. There is sufficient evidence to conclude that the mean price of a single-family home has not changed. C. There is sufficient evidence to conclude that the mean price of a single-family home has decreased. D. There is not sufficient evidence to conclude that the mean price of a single-family home has decreased.

Solution

Solution Steps

Step 1: Hypotheses Formulation

We start by formulating the null and alternative hypotheses based on the problem statement:

Null Hypothesis ($H_0$): The mean price of a single-family home has not decreased, i.e., $\mu \geq 243784$.
Alternative Hypothesis ($H_1$): The mean price of a single-family home has decreased, i.e., $\mu < 243784$.

Step 2: Significance Level

The significance level ($\alpha$) for the hypothesis test is set at $0.05$.

Step 3: Conclusion from the Test

Since the null hypothesis is not rejected, we conclude that there is not sufficient evidence to support the alternative hypothesis. This means we cannot conclude that the mean price of a single-family home has decreased.

Final Answer

The answer is $ \boxed{D} $.

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