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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 鈥渟tandard鈥 significance levels for your significance test, would you choose =0.01, 0.05, or 0.10? Justify your choice.

Short Answer

Expert verified

a. H0:=$85,000-for null hypothesis and Ha:>$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$85000but tests shows it is equal

c.=0.01

Step by step solution

01

introduction

The null hypothesis is an overall explanation that expresses that there is no connection between two peculiarities viable or that there is no relationship between two gatherings. An alternative hypothesis is an explanation that depicts that there is a connection between two chosen factors in a study

02

explanation part (a)

Mean income is $85000

calculating the null and alternative hypotheses,

H0:=$85,000- for null hypothesis

Ha:>$85,000- for alternative hypothesis

hence mean income is equal to $85000and greater than it as per the null and alternative hypotheses respectively.

03

explanation part (b)

Mean income is $85000

Type I error- H0is dismissed when the null hypothesis is valid

The mean income is equivalent to $85000however the test indicates that the mean income is more.

Subsequently, the result is that the caf茅 will open in that location since the mean income is more than the required income, yet in reality, it is not a decent location for the eatery.

Type II error- when the null hypothesis is valid then rejection of H0additionally failed.

The mean income is more than $85000while the test indicates that the mean income is equivalent.

Consequently, the outcome is that the eatery will not open in that location since the mean income is more modest than the required income, yet in reality, it is a decent location for the caf茅.

04

explanation part (c)

To open a restaurant requires a huge investment. Consequently, there is a possibility of making incorrect decisions which can cost a huge amount of cash.

Consequently, a more modest significance level =0.01will be smarter to minimize the probability of making some incorrect decision.

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Most popular questions from this chapter

You read that a statistical test at the =0.01 level has a probability of 0.14 of making a Type II error when a specific alternative is true. What is the power of the test against this alternative?

A 95%confidence interval for a population mean is calculated to be (1.7,3.5). Assume that the conditions for performing inference are met. What conclusion can we draw for a test of role="math" localid="1650275427722" H0:=2versus Ha:2at the A=0.05level based on the confidence interval?

(a) None. We cannot carry out the test without the original data.

(b) None. We cannot draw a conclusion at the A=0.05level since this test is connected to the 97.5%confidence interval.

(c) None. Confidence intervals and significance tests are unrelated procedures.

(d) We would reject H0at level A=0.05.

(e) We would fail to reject H0at level A=0.05.

For the study of Jordanian children in Exercise 4, the sample mean hemoglobin level was 11.3 g/dl and the sample standard deviation was 1.6 g/dl. A significance test yields a P-value of 0.0016.

(a) Interpret the P-value in context.

(b) What conclusion would you make if = 0.05? = 0.01? Justify your answer.

Sampling shoppers A marketing consultant observes 50 consecutive shoppers at a supermarket, recording how much each shopper spends in the store. Explain why it would not be wise to use these data to carry out a significance test about the mean amount spent by all shoppers at this supermarket.

According to the National Institute for Occupational Safety and Health, job stress poses a major threat to the health of workers. In a national survey of restaurant employees, 75% said that work stress had a negative impact on their personal lives. 11 Managers of a large restaurant chain wonder whether this national result holds for their employees. A random sample of 100 employees finds that 68 answered "Yes" when asked, "Does work stress have a negative impact on your personal life?" Is this good reason to think that the proportion of all employees in this chain who would say "Yes" differs from the national proportion of 0.75? Support your answer with a significance test.

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