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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

Critical values What critical value t*from Table B should be used for a

confidence interval for the population mean in each of the following situations?

a. A 95% confidence interval based on n=10 randomly selected observations

b. A99% confidence interval from an SRS of 20 observations

c. A 90% confidence interval based on a random sample of 77 individuals

Age and video games Refer to Exercise 41. The study also estimated that 67% of adults aged 18鈥�29play video games, but only 25%of adults aged 65and older play video games.

a. Explain why you do not have enough information to give confidence intervals for these two age groups separately.

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estimated that 49% of U.S. adults play video games on a computer, TV, game console, or portable device such as a cell phone. This estimate was based on a random sample of 2001 U.S. adults. Construct and interpret a 95% confidence interval for the proportion of all U.S. adults who play video games.

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a. Why is it necessary to check this condition?

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