The following data resulted from a study of randomly chosen major league (a) Give a 95 percent confidence interval estimate for the probability of scoring (b) Give a 95 percent confidence interval estimate for the probability of scoring 294 baseball games played in 1959 and 1960. at least one run when there is a man on first and no outs. at least one run when there is a man on second and one ou Number of Cases in Which 0 Runs Are Scored Total Number of Cases Number of Outs Base Occupied 1,728 1,044 First 401 657 1 Second 48. A random sample of 1,200 engineers included 48 Hispanic Americans, 80 African Americans, and 204 females. Determine 90 percent confidence intervals for the proportion of all engineers who are (a) female; (b) Hispanic Americans or African Americans. 49. To estimate p, the proportion of all newborn babies that are male, the gender of 10,000 newborn babies was noted. If 5,106 of them were male, determine (a). 90 percent and (b) a 99 percent confidence interval estimate of D. 50. An airline is interested in determining the proportion of its customers who are fly- ing for reasons of business. If they want to be 90 percent certain that their estimate will be correct to within 2 percent, how large a random sample should they select? 51. A recent newspaper poll indicated that Candidate A is favored over Candidate B by a 53 to 47 percentage, with a margin of error of +4 then stated that since the 6-point gap is larger than the margin of error, its readers can be certain that Candidate A is the current choice. Is this reasoning correct? percent. The newspaper 52. A market research firm is interested in determining the proportion of households that are watching a particular sporting event. To accomplish this task, they plan on using a telephone poll of randomly chosen households. How large a sample is needed if they want to be 90 percent certain that their estimate is correct to within +.02? 53. In a recent study, 79 of 140 meteorites were observed to enter the atmosphere With a velocity of less than 25 miles per second. If we take p = 79/140 as an estimate of the probability that an arbitrary meteorite that enters the atmosphere will have a speed less than 25 miles per second, what can we say, with 99 percent %3D confidence, about the maximum error of our estimate?