7.11 suppose that we will randomly select a sample of 64 measurements from a population having a mean equal to 20 and a standard deviation equal to 4. a. Describe the shape of the sampling distribution of the sample mean x. Do we need to make any assumptions about the shape of the population? b. Find the mean and the standard deviation of the sampling distribution of the sample mean x c. Calculate the probability that we will obtain a sample mean greater than 21; that is, calculate P(x > 21). d. Calculate the probability that we will obtain a sample mean less than 19.385; that is, calculate P(x < 19.385). 7.30 On February 8, 2002, the Gallup Organization released the results of a poll concerning American attitudes toward the 19th Winter Olympic Games in Salt Lake City, Utah. The poll results were based on telephone interviews with a randomly selected national sample of 1,011 adults, 18 years and older, conducted February 4-6, 2002 a. suppose we wish to use the poll's results to justify the claim that more than 30 percent of Americans (18 years or older) say that figure skating is their favorite Winter Olympic event. The poll actually found that 32 percent of respondents reported that figure skating was their favorite event. If, for the sake of argument, we assume that 30 percent of Americans (18 years or older)say figure skating is their favorite event (that is, p =.3), calculate the probability of observing a sample proportion of .32 or more; that is, P(p > .32) b. based on the probability you computed in part a, would you conclude that more than 30 percent of Americans (18 years or older) say that figure skating is their favorite Winter Olympic event? 8.8 THE BANK CUSTOMER WAITING TIME CASE Recall that a bank manager has develop a new system to reduce the time customers spend waiting to be served by tellers during peak business hours. The mean waiting time during peak business hours under the current system is roughly 9 to 10 minutes. The bank manager hopes that the new system will have a mean waiting time that is less than six minutes. The mean of the sample of 100 bank customers waiting time in Table 1.8 is x = 5.46 we let u denote the mean of all possible bank customer waiting times using the new system and assume that q equals 2.47: a. calculate 95 percent and 99 percent confidence intervals for u b. using the 95 percent confidence interval, can the bank manager be 95 percent confident that u is less than six minutes? c. using the 99 percent confidence interval, can the bank manager be 99 percent confident that u is less than six minutes? d. based on your answers to part b and c, how convinced are you that the new mean waiting time is less than six minutes? Resubmitted my questions and accepted the $30 fee. Can you assist me with these problems.
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