7-2 Estimating a Population Mean 343 18. Arsenic in Rice Listed below are amounts of arsenic (μg, or micrograms, per serving) in samples of brown rice from California (based on data from the Food and Drug Administration). Use a 90% confidence level. The Food and Drug Administration also measured amounts of arsenic in samples of brown rice from Arkansas. Can the confidence interval be used to describe arsenic levels in Arkansas? 5.4 5.6 8.4 7.3 4.5 7.5 1.5 5.5 9.1 8.7 19. Mercury in Sushi An FDA guideline is that the mercury in fish should be below 1 part per million (ppm). Listed below are the amounts of mercury (ppm) found in tuna sushi sampled at different stores in New York City. The study was sponsored by the New York Times, and the stores (in order) are D’Agostino, Eli’s Manhattan, Fairway, Food Emporium, Gourmet Garage, Grace’s Marketplace, and Whole Foods. Construct a 98% confidence interval estimate of the mean amount of mercury in the population. Does it appear that there is too much mercury in tuna sushi? 0.56 0.75 0.10 0.95 1.25 0.54 0.88 20. Caffeine in Soft Drinks Listed below are measured amounts of caffeine (mg per 12 oz of drink) obtained in one can from each of 20 brands (7UP, A&W Root Beer, Cherry Coke, . . . , TaB). Use a confidence level of 99%. Does the confidence interval give us good information about the population of all cans of the same 20 brands that are consumed? Does the sample appear to be from a normally distributed population? If not, how are the results affected? 0 0 34 34 34 45 41 51 55 36 47 41 0 0 53 54 38 0 41 47 Sample Size. In Exercises 21–29, find the sample size required to estimate the population mean. 21. Mean IQ of Statistics Students The Wechsler IQ test is designed so that the mean is 100 and the standard deviation is 15 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of statistics students. We want to be 95% confident that our sample mean is within 3 IQ points of the true mean. The mean for this population is clearly greater than 100. The standard deviation for this population is less than 15 because it is a group with less variation than a group randomly selected from the general population; therefore, if we use s = 15 we are being conservative by using a value that will make the sample size at least as large as necessary. Assume then that s = 15 and determine the required sample size. Does the sample size appear to be practical? 22. Mean IQ of Data Scientists See the preceding exercise, in which we can assume that s = 15 for the IQ scores. Data scientists are a group with IQ scores that vary less than the IQ scores of the general population. Find the sample size needed to estimate the mean IQ of data scientists, given that we want 98% confidence that the sample mean is within 2 IQ points of the population mean. Does the sample size appear to be practical? 23. Ages of Moviegoers Find the sample size needed to estimate the mean age of movie patrons, given that we want 98% confidence that the sample mean is within 1.5 years of the population mean. Assume that s = 19.6 years, based on a previous report from the Motion Picture Association of America. Could the sample be obtained from one movie at one theater? 24. Lengths of Songs The manager for a radio station wants to estimate the mean length of all songs published after 1960. How many songs should be in the sample if we want 99% confidence that the sample mean is within 15 seconds of the population mean? Use the range rule of thumb to estimate s, assuming that the shortest and longest songs are 1.5 minutes and 12 minutes long. 25. Mean Pulse Rate of Males Data Set 1 “Body Data” in Appendix B includes pulse rates of 153 randomly selected adult males, and those pulse rates vary from a low of 40 bpm to a high of 104 bpm. Find the minimum sample size required to estimate the mean pulse rate of adult males. Assume that we want 99% confidence that the sample mean is within 2 bpm of the population mean. continued
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