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Chapter 8: Q.3.2 (page 511)
What inference method will you use? Check that the conditions for using this procedure are met.
Here, population is normal. Thus, the t-confidence interval could be computed here.
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A radio talk show host with a large audience is interested in the proportion of adults in his listening area who think the drinking age should be lowered to eighteen. To find this out, he poses the following question to his listeners: "Do you think that the drinking age should be reduced to eighteen in light of the fact that eighteen-year-olds are eligible for military service?" He asks listeners to phone in and vote "Yes" if they agree the drinking age should be lowered and "No" if not. Of the people who phoned in, answered "Yes." Which of the following conditions for inference about a proportion using a confidence interval are violated?
I. The data are a random sample from the population of interest.
II. is so large that both are at least .
III. The population is at least times as large as the sample.
(a) I only
(c) III only
(c) I, II, and III
(b) II only
(d) I and II only
NAEP scores Refer to Exercise 5. Below your sketch, choose one value of inside the shaded region and draw its corresponding confidence interval. Do the same for one value of outside the shaded region. What is the most important difference between these intervals?
Running red lights A random digit dialing telephone survey ofdrivers asked, "Recalling the last ten traffic lights you drove through, how many of them were red when you entered the intersections?" Of the respondents, admitted that at least one light had been red.
(a) Construct and interpret aconfidence interval for the population proportion.
(b) Nonresponse is a practical problem for this survey-only of calls that reached a live person were completed. Another practical problem is that people may not give truthful answers. What is the likely direction of the bias: do you think more or fewer than of the respondents really ran a red light? Why? Are these sources of bias included in the margin of error?
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
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?
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