Three years ago, the mean price of a single-family home was $\$ 243,712$ A real estate broker believes that the mean price has decreased since then. The null and altemative hypotheses are $\mathrm{H}_{0} \mu=\$ 243,712, \mathrm{H}_{3}, \mu<\$ 243712$ C. A type 1 error would occur if in fact $\mu=\$ 243,712$, but the results of the sampling fail to lead to the conclusion that $\mu<\$ 243,712$. b. Explain what it would mean to make a type il error A. A type 11 error would occur if in fact $\mu=\$ 243,712$, but the results of the sampling lead to the conclusion that $\mu<\$ 243,712$. B. A type II error would occur if in fact $\mu<\$ 243,712$, but the results of the sampling lead to the conclusion that $\mu<\$ 243,712$ C. A type II error would occur if in fact $\mu<\$ 243,712$, but the results of the sampling fall to lead to the conclusion that $\mu<\$ 243,712$ c. Explain what it would mean to make a correct decision A. A correct decision would occur if $\mu \times \$ 243,712$ and the results of the sampling lead to the rejection of that fact, or if $\mu=\$ 243,712$ and the results of the sampling do not lead to that conclusion B. A correct decision would occur if $\mu=\$ 243,712$ and the results of the sampling lead to the rejection of that fact, or if $\mu<\$ 243,712$ and the results of the sampling do not lead to that conclusion C. A correct decision would occur if $\mu=\$ 243,712$ and the tesults of the sampling do not lead to the rejection of that fact, or if $\mu<\$ 243,712$ and the results of the samping lead to that conclusion
Solution
Step 1 ：A Type I error, also known as a false positive, would occur if we reject the null hypothesis when it is actually true. In this case, it would mean concluding that the mean price has decreased (rejecting the null hypothesis) when in fact it has not (the null hypothesis is true).
Step 2 ：A Type II error, also known as a false negative, would occur if we fail to reject the null hypothesis when it is actually false. In this case, it would mean failing to conclude that the mean price has decreased (failing to reject the null hypothesis) when in fact it has (the null hypothesis is false).
Step 3 ：A correct decision would occur if we correctly reject the null hypothesis when it is false, or correctly fail to reject the null hypothesis when it is true. In this case, it would mean correctly concluding that the mean price has decreased when it has, or correctly failing to conclude that the mean price has decreased when it has not.
Step 4 ：Final Answer: Type I error: Concluding that the mean price has decreased when it has not. Type II error: Failing to conclude that the mean price has decreased when it has. Correct decision: Correctly concluding that the mean price has decreased when it has, or correctly failing to conclude that the mean price has decreased when it has not.
