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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⏞1-p⏞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⏞1-p⏞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

In each of the following situations, discuss whether it would be appropriate to construct a one-sample tinterval to estimate the population mean.

(a) We collect data from a random sample of adult residents in a state. Our goal is to estimate the overall percentage of adults in the state who are college graduates.

(b) The coach of a college men’s basketball team records the resting heart rates of the 15team members. We use these data to construct a confidence interval for the mean resting heart rate of all male students at this college.

(c) Do teens text more than they call? To find out, an AP Statistics class at a large high school collected data on the number of text messages and calls sent or received by each of 25randomly selected students. The Fathom boxplot below displays the difference (texts calls) for each student.

Can you taste PTC? PTC is a substance that has a strong bitter taste for some people and is tasteless for others. The ability to taste PTC is inherited. About 75% of Italians can taste PTC, for example. You want to estimate the proportion of Americans who have at least one Italian grandparent and who can taste PTC.

(a) How large a sample must you test to estimate the proportion of PTC tasters within 0.04with 90% confidence? Answer this question using the 75% estimate as to the guessed value for p∧.

(b) Answer the question in part (a) again, but this time use the conservative guess p∧=0.5. By how much do the two sample sizes differ?

True or false: The interval from 2.84to 7.55has a 95%chance of containing the actual population standard deviation S. Justify your answer.

In each of the following settings, check whether the conditions for calculating a confidence interval for the population proportion p are met.

1. An AP Statistics class at a large high school conducts a survey. They ask the first 100 students to arrive at school one morning whether or not they slept at least 8 hours the night before. Only 17 students say "Yes."

2. A quality control inspector takes a random sample of 25 bags of potato chips from the thousands of bags filled in an hour. Of the bags selected, 3 had too much salt.

Watching TV (6.1, 7.3) Choose a young person (aged 19to 25) at random and ask, “In the past seven days, how many days did you watch television?” Call the response Xfor short. Here is the probability distribution for X.

(a) What is the probability that X=7? Justify your answer.

(b) Calculate the mean of the random variable X. Interpret this value in context.

(c) Suppose that you asked 100randomly sele

cted young people (aged 19to 25) to respond to the question and found that the mean xof their responses was 4.96. Would this result surprise you? Justify your answer.

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