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 location. Based on the mean income of this sample, you will decide whether to open a restaurant there.8
(a) State appropriate null and alternative hypotheses. Be sure to define your parameter.
(b) Describe a Type I and a Type II error, and explain the consequences of each.
(c) If you had to choose one of the “standard” significance levels for your significance test, would you choose $α$ = 0.01, 0.05, or 0.10? Justify your choice.

Question

Accepted Answer

a. $H_{0} : μ = $ 85, 000$ -for null hypothesis and $H_{a} : μ > $ 85, 000$ - for alternative hypothesis

b. Type I error- mean income = $$ 85000$ , but tests show it is more. Type II error - mean income greater than $$ 85000$ but tests shows it is equal

c. $α = 0.01$

Short Answer