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Chapter 8: Q. 21 (page 483)

A researcher plans to use a random sample of n=500families to estimate the mean monthly family income for a large population. A99%confidence interval based on the sample would be ______ than a 90% confidence interval.

(a) narrower and would involve a larger risk of being incorrect

(b) wider and would involve a smaller risk of being incorrect

(c) narrower and would involve a smaller risk of being incorrect

(d) wider and would involve a larger risk of being incorrect

(e) wider, but it cannot be determined whether the risk of being incorrect would be larger or smaller

Short Answer

Expert verified

(b) wider and would involve a smaller risk of being incorrect

Step by step solution

01

Given Information

(a) narrower and would involve a larger risk of being incorrect

(b) wider and would involve a smaller risk of being incorrect

(c) narrower and would involve a smaller risk of being incorrect

(d) wider and would involve a larger risk of being incorrect

(e) wider, but it cannot be determined whether the risk of being incorrect would be larger or smaller

02

Explanation

A 99%confidence interval will be wider than a 90%confidence interval because a 99%confidence interval will result in an interval that is more likely to contain the true population mean than the90% confidence interval.

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Most popular questions from this chapter

Got shoes? The class in Exercise 1 wants to estimate the variability in the number of pairs of shoes that female students have by estimating the population variance σ2.

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.

Good wood? A lab supply company sells pieces of Douglas fir 4inches long and 1.5inches square for force experiments in science classes. From experience, the strength of these pieces of wood follows a Normal distribution with standard deviation 3000pounds. You want to estimate the mean load needed to pull apart these pieces of wood to within 1000pounds with 95%confidence. How large a sample is needed? Show your work.

- Understand how the margin of error of a confidence interval changes with the sample size and the level of confidence C.

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.

Got shoes? How many pairs of shoes, on average, do female teens have? To find out, an AP Statistics class conducted a survey. They selected an SRS of 20female students from their school. Then they recorded the number of pairs of shoes that each student reported having. Here are the data:
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