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Chapter 8: Q. T8.4 (page 549)

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 true proportion p of all 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

e. 750

Short Answer

Expert verified

The required smallest number of consumers is 600

The correct option is(b)

Step by step solution

01

Given information

Confidence level =99%

Margin of error(E)=0.05

02

The objective is to find out the smallest number of consumers to have the margin of error at most 0.05at 99%the confidence level.

We know,

The formula to compute the sample size is:

n=p^(1-p^)z伪2E2

There is no information about p^provided here.

Thus, assume is to be 0.50

According to the standard norma table, the value of z伪2corresponding to99%the confidence level is 2.576

The sample size is calculated as follows:

n=p^(1-p^)z伪2E2=0.50(1-0.50)2.5760.052=664

The smallest number of consumers is 600

Therefore, the correct option is(b)

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Most popular questions from this chapter

In preparing to construct a one-sample t interval for a population mean, suppose we are not sure if the population distribution is Normal. In which of the following circumstances would we not be safe constructing the interval based on an SRS of size14from the population?

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