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
a. the mean price of a single family home in any neighborhood is $243,758
b. the mean price of a single family home in the brokers neighborhood is different from $243,758
c. the mean price of a single family home in the brokers neighborhood is $243,758
d. the mean price of a single family home in the brokers neighborhood is greater than $243,758
(b) state the hypotheses symbolically
$h_0: mu = 243758$
$h_1: mu > 243758$
(c) what would it mean to make a type i error?
the broker the hypothesis that the mean price is $, when the true mean price is $

Explanation:

• Type I Error: A Type I error occurs when we reject the null hypothesis \(H_0\) when it 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 broker's neighborhood).
• Interpretation: If a Type I error is made, the broker is rejecting the claim that the mean price of a single - family home in her neighborhood is \(\$243,758\) (the null hypothesis), but in reality, the mean price is \(\$243,758\).

Answer:

The broker rejects the hypothesis that the mean price is equal to \(\$243758\), when the true mean price is equal to \(\$243758\).