Question

Three years​ ago, the mean price of an existing​ single-family home was ​$243, 718. A real estate broker believes that existing home prices in her neighborhood are

lower.

​(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.

Answer 1

The broker thinks that the existing home prices are lower. Thus, clearly, this is a one tailed test.

a.

Thus,

Null hypothesis: H0: mean price of an existing single family home > = $ 243,718.

Alternate hypothesis: Ha: mean price of an existing single family home < $ 243,718.

b.

A type I error is made when we incorrectly reject the null hypothesis; that is, it is made when we reject the null hypothesis when it is actually true.

In our context, a type I error would be made if we hypothesize that the mean price of a home is less than $ 243,718, when in reality it is greater than $ 243,718.

c.

A type II error is made when we incorrectly fail to reject the null hypothesis (or accept the null hypothesis); that is, it is made when we fail to reject the null hypothesis when it is actually false.

In our context, a type II error would be made if we hypothesize that the mean price of a home is greater than or equal to $ 243,718, when in reality it is lesser than $ 243,718.