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Confidence intervals, again Several factors are involved in the creation of a confidence interval. Among them are the sample size, the level of confidence, and the margin of error. Which statements are true? a) For a given sample size, reducing the margin of error will mean lower confidence. b) For a certain confidence level, you can get a smaller margin of error by selecting a bigger sample. c) For a fixed margin of error, smaller samples will mean lower confidence. d) For a given confidence level, a sample 9 times as large will make a margin of error one third as big.

Death penalty, again In the survey on the death penalty you read about in the chapter, the Gallup Poll actually split the sample at random, asking 510 respondents the question quoted earlier, "Generally speaking, do you believe the death penalty is applied fairly or unfairly in this country today?" The other 510 were asked "Generally speaking, do you believe the death penalty is applied unfairly or fairly in this country today?" Seems like the same question, but sometimes the order of the choices matters. Asked the first question, \(58 \%\) said the death penalty was fairly applied; only \(54 \%\) said so with the second wording. a) What kind of bias may be present here? b) If we combine them, considering the overall group to be one larger random sample of 1020 respondents, what is a \(95 \%\) confidence interval for the proportion of the general public that thinks the death penalty is being fairly applied? c) How does the margin of error based on this pooled sample compare with the margins of error from the separate groups? Why?

Amendment A TV news reporter says that a proposed constitutional amendment is likely to win approval in the upcoming election because a poll of 1505 likely voters indicated that \(52 \%\) would vote in favor. The reporter goes on to say that the margin of error for this poll was \(3 \%\) a) Explain why the poll is actually inconclusive. b) What confidence level did the pollsters use?