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Chapter 8: Q.4 (page 524)

Many television viewers express doubts about the validity of certain commercials. In an attempt to answer their critics, Timex Group USA wishes to estimate the proportion of consumers who believe what is shown in Timex television commercials. Let prepresent the true proportion of consumers who believe what is shown in Timex television commercials. What is the smallest number of consumers that Timex can survey to guarantee a margin of error of 0.05or less at a 99%confidence level?

(a) 550

(b) 600

(c) 650

(d) 700

(c)750

Short Answer

Expert verified

(c)650

Step by step solution

01

Step-1 Given Information

Given in the question that,

Mirror of error(E)=5%=0.05

confidence level =99%we have to find the correct option.

02

Step-2 Explanation

The formula to compute the sample size is:

n=p铃�1-p铃�zE2

From the standard normal table, the z-score at 99%confidence level is 2.576

Consider, sample proportion to be0.05.

The sample size is calculated as:

n=p铃�1-p铃�zE2

role="math" localid="1649224673729" =0.501-0.502.5760.052

=664

Here, the smallest sample size is required. Thus, the minimum sample size is 650. Hence, the correct option is (c).

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Most popular questions from this chapter

51. You want to design a study to estimate the proportion of students at your school who agree with the statement, 鈥淭he student government is an effective organization for expressing the needs of students to the administration.鈥� You will use a 95% confidence interval, and you would like the margin of error to be 0.05 or less. The minimum sample size required is
(a) 22. (b) 271. (c) 385. (d) 769. (e) 1795.

Explain briefly why each of the three conditions鈥擱andom, Normal, and Independent鈥攊s important when constructing a confidence interval.

A researcher plans to use a random sample of n=500families to estimate the mean monthly family income for a large population. A99%confidence interval based on the sample would be ______ than a 90% confidence interval.

(a) narrower and would involve a larger risk of being incorrect

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Alcohol abuse has been described by college presidents as the number one problem on campus, and it is an important cause of death in young adults. How common is it? A survey of 10,904 randomly selected U.S. college students collected information on drinking behavior and alcohol-related problems.9 The researchers defined 鈥渇requent binge drinking鈥� as having five or more drinks in row three or more times in the past two weeks. According to this definition, 2486 students were classified as frequent binge drinkers

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