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Chapter 9: Q 99. (page 610)

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 significant test about the mean amount spent by all shoppers at this supermarket.

Short Answer

Expert verified

The sample is a convenience sample.

Step by step solution

01

Given information

Consecutive shoppers: 50

02

Calculation

Because the shoppers were "conveniently" picked as 50 consecutive shoppers, the sample is a convenience sample. These customers shop on the same day of the week and at the same time of day, implying that we may be excluding a portion of the population.

As a result, the sample is not representative of the entire population.

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Most popular questions from this chapter

Which of the following has the greatest probability?

a.P(t>2)if t has 5 degrees of freedom.

b. P(t>2) if t has 2 degrees of freedom.

c. P(z>2) if z is a standard Normal random variable.

d.P(t<2)if t has 5 degrees of freedom.

e.P(z<2) if z is a standard Normal random variable.

A random sample of 100 likely voters in a small city produced 59 voters in favor of Candidate A. The observed value of the standardized test statistic for performing a test of H0:p=0.5H0:p=0.5versus Ha:p>0.5Ha:p>0.5

is which of the following?

a)z=0.59-0.50.59(0.41)100

b)z=0.59-0.50.5(0.5)100

c)z=0.5-0.590.59(0.41)100

d)z=0.5-0.590.5(0.5)100

e)z=0.59-0.5100

Awful accidents Slow response times by paramedics, firefighters, and policemen can have serious consequences for accident victims. In the case of life-threatening injuries, victims generally need medical attention within 8minutes of the accident. Several cities have begun to monitor emergency response times. In one such city, emergency personnel took more than 8minutes to arrive on 22%of all calls involving life-threatening injuries last year. The city manager shares this information and encourages these first responders to 鈥渄o better.鈥� After 6months, the city manager selects an SRS of 400 calls involving life- threatening injuries and examines the response times. She then performs a test at the 伪=0.05level of H0: p=0.22versus Ha:p<0.22, where pis the true proportion of calls involving life-threatening injuries during this 6-month period for which emergency personnel took more than 8minutes to arrive.

a. Describe a Type I error and a Type II error in this setting.

b. Which type of error is more serious in this case? Justify your answer.

c. Based on your answer to part (b), do you agree with the manager鈥檚 choice of 伪=0.05? Why or why not?

An opinion poll asks a random sample of adults whether they favor banning ownership of handguns by private citizens. A commentator believes that more than half of all adults favor such a ban. The null and alternative hypotheses you would use to test this claim are

邪.H0:p鈭�=0.5;Ha:p鈭�>0.5H0:p^=0.5;Ha:p^>0.5.

b. H0:p=0.5;Ha:p>0.5H0:p=0.5;Ha:p>0.5.

c. H0:p=0.5;Ha:p<0.5H0:p=0.5;Ha:p<0.5.

d. H0:p=0.5;Ha:p鈮�0.H0:p=0.5;Ha:p鈮�0.5.

e. H0:p>0.5;Ha:p=0.5H0:p>0.5;Ha:p=0.5.

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.
See all solutions

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