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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

The body mass index (BMI) of all American young women is believed to follow a Normal distribution with a standard deviation of about 7.5. How large a sample would be needed to estimate the mean BMI M in this population to within ±1vwith 99% confidence? Show your work.

Abstain from drinking In a Harvard School of Public Health survey, 2105 of 10,904 randomly selected U.S. college students were classified as abstainers (nondrinkers).

(a) Construct and interpret a 99% confidence interval forp. Follow the four-step process.

(b) A newspaper article claims that 25% of U.S. college students are nondrinkers. Use your result from (a) to comment on this claim.

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.

Scientists collect data on the blood cholesterol levels (milligrams per deciliter of blood) of a random sample of 24laboratory rats. A 95%confidence interval for the mean blood cholesterol level Mis 80.2to 89.8. Which of the following would cause the most worry about the validity of this interval?

(a) There is a clear outlier in the data.

(b) A stemplot of the data shows a mild right skew.

(c) You do not know the population standard deviation S.

(d) The population distribution is not exactly Normal.

(e) None of these would be a problem because the t procedures are robust.

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.
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