Q1. 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? Why or why not.
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).
Q2. 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 year 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, calculate 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?
Q3. THE BANK CUSTOMER WAITING TIME CASE
Recall that a bank manager has developed a new system to reduce the time customers spend waiting to be served by tellers during peak business hours. The mean waiting time during business hours under the current system is roughly 9 to 10 minutes. The bank manager hop. that the new system will have a mean waiting time that is less than six minutes. The mean the sample of 100 bank customer waiting times in Table 1.8 is x‾ = 5.46. If we let µ denote the mean of all possible bank customer waiting times using the new system and assume thic equals 2.47:
a) Calculate 95 percent and 99 percent confidence intervals for μ.
b) Using the 95 percent confidence interval, can the bank manager be 95 percent confident that μ is less than six minutes? Explain.
c) Using the 99 percent confidence interval, can the bank manager be 99 percent confident that μ is less than six minutes? Explain.
d) Based on your answers to parts b and c. How convinced are you that the new mean waiting time is less than six minutes?
Q4. Quality Progress, February 2005, reports on the results achieved by Bank of America in improving customer satisfaction and customer loyalty by listening to the 'voice of the customer.' A key measure of customer satisfaction is the response on a scale from I to 10 to the question: "Considering all the business you do with Bank of America, what is your overall satisfaction with Bank of America?" Suppose that a random sample of 350 current customers results in 195 customers with a response of 9 or 10 representing "customer delight." Find a 95 percent confidence interval for the true proportion of all current Bank of America customers who would respond with a 9 or 10. Are we 95 percent confident that this proportion exceeds .48, the historical proportion of customer delight for Bank of America?