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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

60. Travel time to work A study of commuting times reports the travel times to work of a random sample of 20employed adults in New York State. The mean is x炉=31.25 minutes, and the standard deviation is sx=21.88minutes. What is the standard error of the mean? Interpret this value in context.

How heavy a load (pounds) is needed to pull apart pieces of Douglas fir 4inches long and 1.5inches square? A random sample of 20similar pieces of Douglas fir from a large batch was selected for a science class. The Fathom boxplot below shows the class鈥檚 data. Explain why it would not be wise to use a one-sample t interval to estimate the population mean渭.

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

(b) wider and would involve a smaller risk of being incorrect

(c) narrower and would involve a smaller risk of being incorrect

(d) wider and would involve a larger risk of being incorrect

(e) wider, but it cannot be determined whether the risk of being incorrect would be larger or smaller

What inference method will you use? Check that the conditions for using this procedure are met.

You want to compute a 90%confidence interval for the mean of a population with unknown population standard deviation. The sample size is 30. The value of role="math" localid="1649226392559" tyou would use for this interval is

(a)1.645(b).1.699(c)1.697

(d) 1.96(e) 2.045
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