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. Suppose that for the second way of phrasing it, only 54% said they thought the death penalty was fairly applied.
a) Construct a 95% confidence interval for the true proportion of adults who approve of the way the death penalty is currently applied, according to the responses for this second question.
b) Recall that 60% of the respondents in the other random half of the study said that the death penalty is applied fairly. Does a proportion of 0.60 fall inside the confidence interval you just found?