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Chapter 10: Q. AP3.3 (page 701)

Sports Illustrated planned to ask a random sample of Division I college athletes, 鈥淒o you believe performance-enhancing drugs are a problem in college sports?鈥� Which of the following is the smallest number of athletes that must be interviewed to estimate the true proportion who believe performance-enhancing drugs are a problem within 卤2% with 90% confidence?

a.17b.21c.1680d.1702e.2401

Short Answer

Expert verified

The correct optionis

a.n=z伪/220.25ME2=1.652脳0.250.022鈮�1702

Step by step solution

01

Given information

We have to find the smallest number of athletes that must be interviewed to estimate the true proportion.

02

Explanation 

Formula sample size:

p^known:n=z伪/22p^q^ME2=z伪/22p^(1-p^)ME2

p^unknown:n=z伪/220.25ME2

the sample size is:

n=z伪/220.25ME2=1.652脳0.250.022鈮�1702

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Most popular questions from this chapter

Who talks more鈥攎en or women? Researchers equipped random samples of 56 male and 56 female students from a large university with a small device that secretly records sound for a random 30 seconds during each 12.5-minute period over 2 days. Then they counted the number of words spoken by each subject during each recording period and, from this, estimated how many words per day each subject speaks. The female estimates had a mean of 16,177 words per day with a standard deviation of 7520 words per day. For

the male estimates, the mean was 16,569 and the standard deviation was 9108. Do these data provide convincing evidence at the 伪=0.053051526=0.200=20.0%伪=0.05significance level of a difference in the average number of words spoken in a day by all male and all female students at this university?

An SRS of size 100is taken from Population A with proportion 0.8of successes. An independent SRS of size 400is taken from Population B with proportion 0.5of successes. The sampling distribution of the difference (A 鈭� B) in sample proportions has what mean and standard deviation?

a. mean=0.3; standard deviation =1.3

b. mean=0.3; standard deviation =0.40

c. mean=0.3; standard deviation =0.047

d. mean=0.3; standard deviation =0.0022

e. mean=0.3; standard deviation =0.0002

Friday the 13thRefer to Exercise 88.

a. Construct and interpret a 90%confidence interval for the true mean difference. If you already defined parameters and checked conditions in Exercise 88, you don鈥檛 need to do them again here.

b. Explain how the confidence interval provides more information than the test in Exercise 88.

Digital video disks A company that records and sells rewritable DVDs wants to compare the reliability of DVD fabricating machines produced by two different manufacturers. They randomly select 500DVDs produced by each fabricator and find that 484of the disks produced by the first machine are acceptable and 480of the disks produced by the second machine are acceptable. If p1,p2are the proportions of acceptable DVDs produced by the first and second machines, respectively, check if the conditions for calculating a confidence interval for p1-p2are met.

Don鈥檛 drink the water!The movie A Civil Action (1998) tells the story of a

major legal battle that took place in the small town of Woburn, Massachusetts. A town well that supplied water to east Woburn residents was contaminated by industrial chemicals. During the period that residents drank water from this well, 16of 414babies born had birth defects. On the west side of Woburn, 3of 228babies born during the same time period had birth defects. Let p1be

the true proportion of all babies born with birth defects in west Woburn and p2be the true proportion of all babies born with birth defects in east Woburn. Check if the conditions for calculating a confidence interval forp1-p2are met.
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