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Chapter 8: Q.10 (page 523)
It's about ME Explain how each of the following would affect the margin of error of a confidence interval, if all other things remained the same.
(a) Increasing the confidence level
(b) Quadrupling the sample size
(a) It increases the margin of error.
(b) It would reduce the margin of error.
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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 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.
A TV poll A television news program conducts a call-in poll about a proposed city ban on handgun ownership. Of the calls, oppose the ban. The station, following recommended practice, makes a confidence statement: of the Channel Pulse Poll sample opposed the ban. We can be confident that the true proportion of citizens opposing a handgun ban is within of the sample result."
(a) Is the station's quoted margin of error correct? Explain.
(b) Is the station's conclusion justifed? Explain.
Refer to Exercise . As Gallup indicates, the percentage point margin of error for this poll includes only sampling variability (what they call “sampling error”). What other potential sources of error (Gallup calls these “non-sampling errors”) could affect the accuracy of the estimate?
56. The SAT again High school students who take the SAT Math exam a second time generally score higher than on their first try. Past data suggest that the score increase has a standard deviation of about points.
How large a sample of high school students would be needed to estimate the mean change in SAT score to within points with confidence? Show your work.
2K10 begins In January , a Gallup Poll asked a random sample of adults, "In general, are you satisfied or dissatisfied with the way things are going in the United States at this time?" In all, said that they were sitisfied and the remaining said they were not. Construct and interpret aconfidence interval for the proportion of adults who are satisfied with how things are going. Follow the four-step process.
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