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Chapter 9: Q 90. (page 609)

Restaurant power problems Refer to Exercises 86 and 88

a. Explain one disadvantage of using 伪=0.10 instead of 伪=0.05 when

performing the test.

b. Explain one disadvantage of taking a random sample of 50 people instead of 30 people.

Short Answer

Expert verified

Part (a) There is the most likely to have a type I error.

Part (b) There is more time consuming and costly to collect the data.

Step by step solution

01

Part (a) Step 1: Given information

伪=0.05H0:渭=$85,000渭>$85,000渭=$86,000
02

Part (a) Step 2: Explanation

Type I error: Reject the null hypothesis H0, once the null hypothesis H0is true.

伪Showing the probability of a type I error.

If you increase 伪=0.05to伪=0.10 the likelihood of making a type I error increases, and you're more likely to make one, which is a negative.

03

Part (b) Step 1: Explanation

If the sample size is increased from 30to 50persons, collecting data for the 50people will take longer and cost more money than collecting data for the 30people (as there are about twice as many potatoes about which we need to gather information.).

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Most popular questions from this chapter

More lefties?In the population of people in the United States, about 10% are left-handed. After bumping elbows at lunch with several left-handed students, Simon wondered if more than 10%of students at his school are left-handed. To investigate, he selected an SRS of 50students and found 8lefties (p铃�=8/50=0.16).

To determine if these data provide convincing evidence that more than 10%of the students at Simon鈥檚 school are left-handed, 200trials of a simulation were conducted. Each dot in the graph shows the proportion of students that are left-handed in a random sample of 50students, assuming that each student has a 10%chance of being left handed.

a. State appropriate hypotheses for performing a significance test. Be sure to define the parameter of interest.

b. Use the simulation results to estimate the P-value of the test in part (a). Interpret the P-value.

c. What conclusion would you make?

Do you Tweet? The Pew Internet and American Life Project asked a random sample of U.S. adults, 鈥淒o you ever 鈥� use Twitter or another service to share updates about yourself or to see updates about others?鈥� According to Pew, the resulting 95% confidence interval is (0.123, 0.177).11 Based on the confidence interval, is there convincing evidence that the true proportion of U.S. adults who would say they use Twitter or another service to share updates differs from 0.17? Explain your reasoning.

Side effects A drug manufacturer claims that less than 10%of patients who take its new drug for treating Alzheimer鈥檚 disease will experience nausea. To test this claim, researchers conduct an experiment. They give the new drug to a random sample of 300out of 5000Alzheimer鈥檚 patients whose families have given informed consent for the patients to participate in the study. In all, 25of the subjects experience nausea.

a. Describe a Type I error and a Type II error in this setting, and give a possible

consequence of each.

b. Do these data provide convincing evidence for the drug manufacturer鈥檚 claim?

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?

The reason we use t procedures instead of z procedures when carrying out a test about a population mean is that

a. z requires that the sample size be large.

b. z requires that you know the population standard deviation 蟽

c. z requires that the data come from a random sample.

d. z requires that the population distribution be Normal.

e. z can only be used for proportions.
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