Instructions: This problem set is due by the end of class on Thursday, November 15th. You can either hand in a paper copy, or email a copy to [email protected]. When you submit through email, please title the file "firstname_lastname_ps5". NO LATE homework will be acknowledged. The complete answer comprises not just a numerical (or graphical or tabular) answer, however an interpretation of the result. You are expected to give thorough answers to problems which ask for a discussion, interpretation or description. The overall problem set grade depends mainly on your capability to describe.
problem: (Anderson, Sweeney, and Williams, 11th ed, 8.8)
The National Quality Research Center at University of Michigan offers a quarterly measure of consumer opinions regarding products and services (The Wall Street Journal, February 18, 2003). The survey of 10 restaurants in the Fast Food/Pizza group showed a sample mean customer satisfaction index of 71. Past data point out that the population standard deviation of the index has been relatively stable with σ = 5
a) What assumption must the researcher be willing to make if a margin of error is desired?
b) Using 95% confidence, determine the margin of error?
c) Determine the margin of error if 99% confidence is desired?
problem: (Anderson, Sweeney, and Williams, 11th ed, 8.10)
Playbill magazine reported that the mean annual household income of its readers is $119,155 (Playbill, January 2006). Suppose this estimate of the mean annual household income is based on the sample of 80households, and based on past studies, the population standard deviation is known to be σ = $30; 000.
a) Make a 90% confidence interval estimate of the population mean.
b) Make a 95% confidence interval estimate of the population mean.
c) Make a 99% confidence interval estimate of the population mean.
d) Discuss what happens to the width of confidence interval as the confidence level is raised.
Does this result seem reasonable? Describe.
problem: (Anderson, Sweeney, and Williams, 11th ed, 8.16)
The mean number of hours of flying time for pilots at the Continental Airlines is 49 hours per month (The Wall Street Journal, February 25, 2003). Suppose that this mean was based on actual flying times for a sample of 100 Continental pilots and that the sample standard deviation was 8.5 hours.
a) At 95% confidence, determine the margin of error?
b) Determine the 95% confidence interval estimate of the population mean flying time for the pilots?
c) The mean number of hours of flying time for the pilots at United Airlines is 36 hours per month. Use your outcomes from part (b) to discuss differences between the flying times for the pilots at the two 1airlines. The Wall Street Journal reported United Airlines as having the highest labor cost among all airlines. Does the information in this exercise give insight as to why United Airlines might expect the higher labor costs?
problem: (Anderson, Sweeney, and Williams, 11th ed, 8.19)
The average cost per night of a hotel room in the New York City is $273 (SmartMoney, March 2009). Suppose this estimate is based on the sample of 45 hotels and which the sample standard deviation is $65.
a) With 95% confidence, determine the margin of error?
b) Determine the 95% confidence interval estimate of the population mean?
c) Two years ago, the average cost of a hotel room in the New York City was $229. Discuss the change in cost over two-year period.
problem: (Anderson, Sweeney, and Williams, 11th ed, 8.26)
The average cost of gallon of unleaded gasoline in the Greater Cincinnati was reported to be $2.41 (The Cincinnati Enquirer, February 3, 2006). Throughout periods of rapidly modifying prices, the newspaper samples service stations and prepares reports on gasoline prices frequently. Suppose the standard deviation is $.15 for the price of a gallon of unleaded regular gasoline, and recommend the suitable sample size for the newspaper to use if they wish to report a margin of error at 95% confidence.
a) Assume that the desired margin of error is $.07.
b) Assume that the desired margin of error is $.05.
c) Assume that the desired margin of error is $.03.
problem: (Anderson, Sweeney, and Williams, 11th ed, 8.38)
According to Thomson Financial, through January 25, 2006, the majority of companies reporting profits had beaten estimates (Business Week, February 6, 2006). The sample of 162 companies showed 104 beat estimates, 29 matched estimates, and 29 fell short.
a) What is the point estimate of the proportion which fell short of estimates?
b) Determine the margin of error and provide a 95% confidence interval for the proportion which beat estimates.
c) How big a sample is required if the desired margin of error is .05?