Three years ago, the mean price of an existing single-family home was $243 comma 772. A real estate broker believes that existing home prices in her neighborhood are higher. (a) Determine the null and alternative hypotheses. (b) Explain what it would mean to make a Type I error. (c) Explain what it would mean to make a Type II error

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26-03-2020
Mathematics

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Three years ago, the mean price of an existing single-family home was $243 comma 772. A real estate broker believes that existing home prices in her neighborhood are higher. (a) Determine the null and alternative hypotheses. (b) Explain what it would mean to make a Type I error. (c) Explain what it would mean to make a Type II error

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sonu5678 sonu5678 · Answer 1 · 2020-03-30T17:57:07+02:00

Answer:

(a)

[tex]\mathbf{H_0: p=\$243,772\\H_1: p<\$243,772}[/tex]

(b) The broker rejects the hypothesis that the mean price is $243,772, when it is the true mean cost.

(c) The broker fails to reject the hypothesis that the mean price is $243,772, when the true mean price is less than $243,772.

Step-by-step explanation:

(a) The null and alternative hypotheses are:

[tex]H_0: p=\$243,772\\H_1: p<\$243,772[/tex]

(b) The type I error says that reject the [tex]H_0[/tex] when it is true.

Thus, type I error is: The broker rejects the null hypothesis that the mean price of home is $243,772, when it is the true mean cost.

(c) The type II error says that accept the [tex]H_0[/tex] when it is false.

Thus, type II error is: The broker fails to reject the null hypothesis that the mean price of single-single home is $243,772, when the true mean price is less than $243,772.