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1.       The college Board  American College Testing  Program reported  a population mean SAT score of M= 1020. Assume that the population standard deviation is 100. a.       What is the probability that a random sample of 75 students will provide a sample mean SAT score within 10 of the population mean? b.      What is the probability a random sample of 75 students will provide a sample mean SAT score within 20 of the population mean? 1  2.       Which would be hardest for you to give up: Your computer or your television?  In a recent survey of 1677 U.S. Internet users, 74% of the  young  tech elite(average age of 22) say their computer would be very hard to give up. Only 48% say  their  television would be very hard  to give up. a.       Develop a 95% confidence interval for the proportion of the young tech elite that would find it very hard to give up their computer. b.      Develop a 99% confidence interval for the proportion of the young tech elite that would find it very hard to give up their computer. c.       In which case, part(a) or (b), is the margin of error larger? Explain why?   3.       An extensive study of the cost of health care in the Unite States presented data showing that the mean spending per Medicare enrollee in 2003 was $6883. To investigate differences across the country, a researcher took a sample of 40 Medicare enrollees in Indianapolis. For the Indianapolis spending was $5980 and the standard deviation was $2518. a.       State the hypotheses that should be used if we would like to determine whether the mean annual Medicare spending in Indianapolis is lower than the national mean. b.      Use the preceding sample results to compute the test statistic and the  P-value. c.       Use alpha=0.05. What is your conclusion? d.      Repeat the hypothesis test using the critical value approach.