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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 \(85,000to support the type of upscale restaurant you wish to open. You decide to take a simple random sample of 50people living near one potential location. Based on the mean income of this sample, you will perform a test of

H0:=\)85,000

Ha:>$85,000

where 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

Expert verified

Once null hypothesis H0is true, type Ierror is rejecting null hypothesis H0.

Once null hypothesis H0is false, type IIerror fail to reject null hypothesis H0

Step by step solution

01

Given Information

It is given that n=50

H0:=$85,000

H1:>$85,000

02

Explanation

Once null hypothesis H0is true, type one error is rejecting null hypothesis H0

We have convincing proof that mean financial gain of these living close to restaurant is larger than 85000once 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 H0is false, type IIerror fail to reject H0

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.

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Most popular questions from this chapter

Based on the P-value in Exercise 31, which of the following would be the most

appropriate conclusion?

a. Because the P-value is large, we reject H0. We have convincing evidence that more than 50%of city residents support the tax increase.

b. Because the P-value is large, we fail to reject H0. We have convincing evidence that more than 50%of city residents support the tax increase.

c. Because the P-value is large, we reject H0. We have convincing evidence that at most 50%of city residents support the tax increase.

d. Because the P-value is large, we fail to reject H0. We have convincing evidence that at most 50%of city residents support the tax increase.

e. Because the P-value is large, we fail to reject H0. We do not have convincing

evidence that more than 50%of city residents support the tax increase.

Experiments on learning in animals sometimes measure how long it takes mice to find their way through a maze. The mean time is 18 seconds for one particular maze. A researcher thinks that a loud noise will cause the mice to complete the maze faster. She measures how long each of 10 mice takes with a loud noise as stimulus. The appropriate hypotheses for the significance test are

a. H0:=18;Ha:18

b. H0:=18;Ha:>18

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(a)z=0.64-0.50.64(0.36)100z=0.64-0.50.64(0.36)100

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(c)z=0.64-0.50.5(0.5)100z=0.64-0.50.5(0.5)100

(d)z=0.64-0.50.64(0.36)64z=0.64-0.50.64(0.36)64

(e)z=0.5-0.640.5(0.5)100z=0.5-0.640.5(0.5)100

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