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Chapter 8: Q. 24 (page 484)

A polling organization announces that the proportion of American voters who favor congressional term limits is 64%, with a 95%confidence margin of error of 3%. If the opinion poll had announced the margin of error for 80% confidence rather than 95%confidence, this margin of error would be

(a) 3%, because the same sample is used.

(b) less than 3%, because we require less confidence.

(c) less than 3%, because the sample size is smaller.

(d) greater than 3%, because we require less confidence.

(e) greater than 3%, because the sample size is smaller.

Short Answer

Expert verified

(b) less than 3%, because we require less confidence

Step by step solution

01

Given Information

(a) 3%, because the same sample is used.

(b) less than 3%, because we require less confidence.

(c) less than 3%, because the sample size is smaller.

(d) greater than 3%, because we require less confidence.

(e) greater than 3%, because the sample size is smaller.

02

Explanation

The confidence level is decreased from 95%to 80%. This would then mean that the confidence interval becomes less accurate, that is, we require less confidence/accuracy and thus the confidence interval also becomes less wide.

If the confidence interval becomes less wide, then the margin of error decreases, and thus the margin of error will be less than 3%.

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Most popular questions from this chapter

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.

Abstain from drinking Describe a possible source of error that is not included in the margin of error for the 99%confidence interval in Exercise 35

Watching TV (6.1, 7.3) Choose a young person (aged 19to 25) at random and ask, 鈥淚n the past seven days, how many days did you watch television?鈥� 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.

A TV poll A television news program conducts a call-in poll about a proposed city ban on handgun ownership. Of the 2372 calls, 1921 oppose the ban. The station, following recommended practice, makes a confidence statement: "81%of the Channel 13 Pulse Poll sample opposed the ban. We can be 95% confident that the true proportion of citizens opposing a handgun ban is within1.6% of the sample result."

(a) Is the station's quoted 1.6% margin of error correct? Explain.

(b) Is the station's conclusion justifed? Explain.

Use Table B to find the critical value t* that you would use for a confidence interval for a population mean M in each of the following situations. If possible, check your answer with technology.

(a) A 98% confidence interval based on n=22observations.

(b) A 90%confidence interval from an SRS of 10observations.

(c) A 95% confidence interval from a sample of size7.
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