Question

Three years​ ago, the mean price of an existing​ single-family home was

​$243,759

A real estate broker believes that existing home prices in her neighborhood are

lowerlower.

​(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

a) The null hypothesis will be the mean existing prices in her neighbourhood are not different than they were three years ago. (i.e. $243,759). Whereas, alternative hypothesis will be what broker' belief that current mean home prices are lower. in other words

b) The type I error is an error of rejection null hypothesis when it is true. Thus in our situation, the type I error is the error of broker' belief of lower house prices is accepted when in reality the prices are the same as that of 3 years ago.

c) Type II error happens when one accepts the null hypothesis despite it being wrong. Our context identify such error as coming to the conclusion that current house prices are the same as they were 3 years ago (i.e. $243759) when in reality, the current house prices are lower (as believed by broker).