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Q1: Which measure of central tendency would be most useful in each of the following instances?
(a) The production manager for a manufacturer of glass jars, who is concerned about the proper jar size to manufacture, has sample data on jar sizes ordered by customers. Would the mean, median, or modal jar size be of most value to the manager?
(b) The sales manager for a quality furniture manufacturer is interested in selecting the regions most likely to purchase his firm¡¯s products. Would he be most interested in the mean or median of family income in prospective sales areas?
(c) A security analyst is interested in describing the daily market price change of the common stock of a manufacturing company. Rarely the market price of the stock changes by more than one point, but occasionally the price will change by as many as four points in one day. Should the security analyst describe the daily price change of the stock in terms of the mean, median, or mode of daily market price change?
Q2: Late payment of medical claims can add to the cost of health care. An article reported that the mean time from the date of service to the date of payment for one insurance company was 41.4 days during a recent period. Suppose that a sample of 100 medical claims is selected during the latest time period. The sample mean time from the date of service to the date of payment was 39.6 days, and the sample standard deviation was 7.4 days.
a. Using the 0.05 level of significance, is there evidence that the population mean has changed from 41.4 days?
b. What is your answer in (a) if you use the 0.01 level of significance?
c. What is your answer in (a) if the sample mean is 38.2 days and the sample standard deviation is 10.7 days?
Q3: La Quinta Motor Inns developed a computer model to predict the profitability of sites that are being considered as locations for new hotels. If the computer model predicts large profits, La Quinta buys the proposed site and builds a new hotel. If the computer model predicts small or moderate profits, La Quinta chooses not to proceed. This decision-making procedure can be expressed in the hypothesis-testing framework. The null hypothesis is that the site is not a profitable location. The alternative hypothesis is that the site is a profitable location.
a. Explain the risks associated with committing a Type I error in this case.
b. Explain the risks associated with committing a Type II error in this case.
c. Which type of error do you think the executives at La Quinta Motor Inns are trying hard to avoid? Explain.
Q4: The chair of the accounting department wants to develop a regression model to predict the grade point average in accounting for graduating accounting majors, based on the students¡¯ SAT score and whether the student received a grade of B or higher in the introductory statistics course (0 = no and 1 = yes).
a. Explain the steps involved in developing a regression model for these data. Be sure to indicate the particular models you need to evaluate and compare.
b. Suppose the regression coefficient for the variable of whether the student received a grade of B or higher in the introductory statistics course is +0.30, how do you interpret this result?