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In a survey on supernatural experiences, 722 of 4013 adult Americans reported that they had seen a ghost ("What Supernatural Experiences We've Had," USA TODAY, February 8,2010 ). Assume that this sample is representative of the population of adult Americans. a. Use the given information to estimate the proportion of adult Americans who would say they have seen a ghost. b. Verify that the conditions for use of the margin of error formula to be appropriate are met. c. Calculate the margin of error. d. Interpret the margin of error in context. e. Construct and interpret a \(90 \%\) confidence interval for the proportion of all adult Americans who would say they have seen a ghost. f. Would a \(99 \%\) confidence interval be narrower or wider than the interval calculated in Part (e)? Justify your answer.

Describe how each of the following factors affects the width of the large- sample confidence interval for \(p\) : a. The confidence level b. The sample size c. The value of \(\hat{p}\)

A consumer group is interested in estimating the proportion of packages of ground beef sold at a particular store that have an actual fat content exceeding the fat content stated on the label. How many packages of ground beef should be tested in order to have a margin of error of \(0.05 ?\)