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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High tuition costs Glenn wonders what proportion of the students at his school think that tuition is too high. He interviews an SRS of of the students at his college. Thirty-eight of those interviewed think tuition is too high.
School vouchers A national opinion poll found that % of all American adults agree that parents should be given vouchers that are good for education at any public or private school of their choice. The result was based on a small sample.
(a) How large an SRS is required to obtain a margin of error of (that is, ) in a % confidence interval? Answer this question using the previous poll’s result as the guessed value for .
(b) Answer the question in part (a) again, but this time use the conservative guess . By how much do the two sample sizes differ?
A polling organization announces that the proportion of American voters who favor congressional term limits is , with a confidence margin of error of . If the opinion poll had announced the margin of error for 80% confidence rather than confidence, this margin of error would be
(a) , because the same sample is used.
(b) less than , because we require less confidence.
(c) less than , because the sample size is smaller.
(d) greater than , because we require less confidence.
(e) greater than , because the sample size is smaller.
Election polling Gloria Chavez and Ronald Flynn are the candidates for mayor in a large city. We want to estimate the proportion of all registered voters in the city who plan to vote for Chavez with % confidence and a margin of error no greater than . How large a random sample do we need? Show your work.
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 “frequent binge drinking” 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
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