c. (answer C): A correct decision would occur if u = $243,734 and the results of

Question

c. (answer C): A correct decision would occur if u = $243,734 and the results of the sampling do not lead to the rejection of that? fact; or if u> $243,734 and the resuluts of the sampling lead to that conclusion

Three years ago, the mean price of a single-family home was $243,734. A real estate broker believes that the mean price has increased since then. The null and alternative hypotheses are Ho: HE$243,734, Ha: u $243,734. a. Explain what it would mean to make a type l error. O A. A type l error would occur if in fact H $243,734, but the results of the sampling lead to the conclusion that H $243,734. O B. A type l error would occur if in fact u $243,734, but the results of the sampling lead to the conclusion that H $243,734. O C. A type l error would occur if in fact HE$243,734, but the results of the sampling fail to lead to the conclusion that H $243.734 b. Explain what it would mean to make a type ll error. O A. A type Il error would occur if in fact H> $243,734, but the results of the sampling lead to the conclusion that H $243,734. o B. A type ll error would occur if in fact H-$243,734, but the results of the sampling lead to the conclusion that H >$243,734. ell error would occur if in fact H $243,734, but the results of the sampling fail to lead to the conclusion that H $243,734 A type c. Explain what it would mean to make a correct decision. O A. A correct decision would occur if $243,734 and the results of the sampling lead to the rejection of that fact, or if $243,734 and the results of the sampling do not lead to that conclusion. O B. A correct decision would occur if $243,734 and the results of the sampling lead to the rejection of that fact, or if H $243,734 and the results of the sampling do not lead to that conclusion.

Explanation / Answer

Solution:

We know that the type I error is the probability of rejecting the null hypothesis H0 when it is true and the type II error is the probability of do not rejecting the null hypothesis H0 when it is not true.

Type I error = P(Reject H0 | H0 is true)

Type II error = P(Do not reject H0 | H0 is not true)

Now, by using this definition we have to answer the following questions.

Part a

Explain what it would mean to make a type I error.

Answer:

A.

A type I error would occur if in fact µ = $243,734, but the results of the sampling lead to the conclusion that µ > $243,734.

Part b

Explain what it would mean to make a type II error.

Answer:

C.

A type II error would occur if in fact µ > $243,734, but the results of the sampling fail to lead to the conclusion that µ > $243,734.

Part c

Explain what it would mean to make a correct decision.

Answer:

C.

A correct decision would occur if µ = $243,734 and the results of the sampling do not lead to the rejection of that fact; or if µ > $243,734 and the results of the sampling lead to that conclusion.

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