Consider Exercise 8.39 and suppose we wish to find the sample size n needed in order to be 95 percent confident that the sample proportion of respondents who said they took part in some sort of daily activity to keep physically fit, is within a margin of error of .02 of p, the proportion of all U. S. adults who say that they take part in such activity. In order to find an appropriate value for p(1 – p), note that the 95 percent confidence interval for p that you calculated in Exercise 8.39 was [. 57, .63]. This indicates that the reasonable value for p that is closest to .5 is .57, and thus the largest reasonable value for p(1 – p) is .57(1 – .57) = .2451. Calculate the required sample size n.
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