Question

Upscale restaurant You are thinking about opening a restaurant and are searching for a good location. From the research you have done, you know that the mean income of those living near the restaurant must be over $\backslash (85,000$to support the type of upscale restaurant you wish to open. You decide to take a simple random sample of $50$people living near one potential site. Based on the mean income of this sample, you will perform a test at the

$\alpha =0.05$ significance level of $H_0:\mu =\backslash )85,000$versus $H_a:\mu >\backslash (85,000$, where $\mu$ is the true mean income in the population of people who live near the restaurant. The power of the test to detect that $\mu =\backslash )86,000$is $0.64$ Interpret this value.

Short answer

There is $64$ percent probability that finds the convincing proof to help the alternative hypothesis$\mu >\$85000$

Step-by-step solution

Given information

$$\begin{gathered} H_0:\mu =\$85000 \\ {H}_1:\mu >\$85000 \\ {\mu }_A=alternativemean=\$86000 \end{gathered}$$

$\alpha =significancelevel=0.05$

Power $=0.64=64\%$

Concept

When the alternative hypothesis is true, the power is the probability of rejecting the null hypothesis.

Explanation

If the genuine mean income in the population of persons who live near the restaurant is $\$86000$ there is a $64$ percent chance that the alternative hypothesis $\mu >\$85000$ will be supported.