Question

Opening a restaurant You are thinking about opening a restaurant and are

searching for a good location. From 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 location. Based on the mean income of this sample, you will perform a test of

$H_0:\mu =\backslash )85,000$

$H_a:\mu >\$85,000$

where $\mu$is the true mean income in the population of people who live near the restaurant. Describe a Type $I$ error and a Type $II$ error in this setting, and give a possible consequence of each.

Short answer

Once null hypothesis $H_0$is true, type $I$error is rejecting null hypothesis $H_0$.

Once null hypothesis $H_0$is false, type $II$error fail to reject null hypothesis $H_0$

Step-by-step solution

Given Information

It is given that $n=50$

$H_0:\mu =\$85,000$

$H_1:\mu >\$85,000$

Explanation

Once null hypothesis ${\mathrm{H}}_0$is true, type one error is rejecting null hypothesis $H_0$

We have convincing proof that mean financial gain of these living close to restaurant is larger than $85000$once mean financial gain of these living close to restaurant is actually $85000$.

Double consequence is that opening restaurant in this area where financial gain of people is not enough and hence restaurant can depart of business.

One null hypothesis $H_0$is false, type $II$error fail to reject $H_0$

There is not enough convincing proof that mean financial gain of these living close to restaurant is larger than $85000$, once mean financial gain of these living close to restaurant is actually $85000$.

Double consequence is that not opening restaurant in this area where financial gain of people is large enough and hence it can miss profitable location.