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Chapter 8: Q.1.3 (page 476)
True or false: The interval from to has a chance of containing the actual population standard deviation . Justify your answer.
The provided statement is false.
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Alcohol abuse has been described by college presidents as the number one problem on campus, and it is an important cause of death in young adults. How common is it? A survey of 10,904 randomly selected U.S. college students collected information on drinking behavior and alcohol-related problems.9 The researchers defined 鈥渇requent binge drinking鈥� as having five or more drinks in row three or more times in the past two weeks. According to this definition, 2486 students were classified as frequent binge drinkers.
Interpret the interval in context. Putting It All Together
Equality for women? Have efforts to promote equality for women gone far enough in the United States? A poll on this issue by the cable network MSNBC contacted adults. A newspaper article about the poll said, 鈥淩esults have a margin of sampling error of plus or minus 3 percentage points.鈥�
(a) The news article said that % of men, but only % of women, think that efforts to promote equality have gone far enough. Explain why we do not have enough information to give con铿乨ence intervals for men and women separately.
(b) Would a % con铿乨ence interval for women alone have a margin of error less than , about equal to , or greater than ? Why? (You see that the news article鈥檚 statement about the margin of error for poll results is a bit misleading.)
Good wood? A lab supply company sells pieces of Douglas fir inches long and inches square for force experiments in science classes. From experience, the strength of these pieces of wood follows a Normal distribution with standard deviation pounds. You want to estimate the mean load needed to pull apart these pieces of wood to within pounds with 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 .
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.
Interpret the confidence level.
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