Question

three years ago, the mean price of an existing single - family home was $243,758. a real estate broker believes that existing home prices in her neighborhood are higher
(a) state the null and alternative hypotheses in words.
(b) state the null and alternative hypotheses symbolically.
(c) explain what it would mean to make a type i error.
(d) explain what it would mean to make a type ii error.

d. the mean price of a single family home in the brokers neighborhood is greater than $243,758.
(b) state the hypotheses symbolically.
$h_0: mu = \\$243758$
$h_1: mu>\\$243758$
(type integers or decimals. do not round.)
(c) what would it mean to make a type i error?
the broker rejects the hypothesis that the mean price is equal to $243758, when the true mean price is equal to $243758.
(type integers or decimals. do not round.)
(d) what would it mean to make a type ii error?
the broker the hypothesis that the mean price is $, when the true mean price is $
(type integers or decimals. do not round.)

Explanation:

A Type II error occurs when we fail to reject the null hypothesis \(H_0\) when the alternative hypothesis \(H_1\) is actually true. In this context, the null hypothesis \(H_0:\mu = 243758\) (where \(\mu\) is the mean price of a single - family home in the neighborhood) and the alternative hypothesis \(H_1:\mu>243758\).

Answer:

The broker fails to reject the hypothesis that the mean price is equal to \( \$243758\), when the true mean price is greater than \( \$243758\).