Question

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 $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 significance level of versus where is the true mean income in the population of people who live near the restaurant. The power of the test to detect that is 0.64. Interpret this value.
Required:
Describe a Type 1 and a Type II error.

Answer 1

A type I and type II error of the given question are respectively;

A) concluding that the local mean income exceeds $45000 when in fact it does not and therefore opening a restaurant in a locale that would not support it.

B) concluding that the local mean income does not exceed $45000 when in fact it does not and therefore deciding not to open a restaurant in a locale that would support it.

What is Type 1 and a Type II error?

In statistics, a type I error simply means rejecting the null hypothesis when it's actually true. Meanwhile, a Type II error means failing to reject the null hypothesis when it's actually false.

Now, in this question what we will consider to be a type I error is concluding that the local mean income exceeds $45000 when in fact it does not and therefore opening a restaurant in a locale that would not support it.

A type II error will be concluding that the local mean income does not exceed $45000 when in fact it does not and therefore deciding not to open a restaurant in a locale that would support it.

Read more about Type I and II errors at; brainly.com/question/16012410