102年國立中興大學行銷所統計學

State whether each of the following variables is qualitative of quantitative and indicate its measurement scale.
(1) Annual sales 
(2) Soft-drink size (small, medium, large) 
(3) Employee classification 
(4) Earnings per share 
(5) Method of payment (cash, credit card)

Client Satisfaction Survey for company A asked clients to indicate how satisfied they were with their service quality. Client responses were coded 1 to 7, with 1 indicating “not at all satisfied” and 7 indicating “extremely satisfied.” Assume that the following data are from a sample of 60 responses for a particular service quality.

(1) Comment on why these data are qualitative. 
(2) Provide a frequency distribution and a relative frequency distribution for the date. 
(3) Provide a bar graph. 
(4) On the basis of your summaries, comment on the clients’ overall evaluation of the service quality.

Consider a variation of the decision tree. The company must first decide whether to undertake the market research study. If the market research study is conducted, the outcome will either be favorable (F) or unfavorable (U) . Assume there are only two decision alternatives 1 d and 2 d and two states of nature 1 s and 2 s . The payoff table showing profit is as follows:

(1) Show the decision tree. 
(2) Use the following probabilities. What is the optimal decision strategy?

The five-year historical prices per share for a particular stock and the Consumer Price Index with a 1992-1994 base period follow.

Deflate the stock price series and comment on the investment aspects of this stock.

The Year Chemical Company wants to estimate the mean time (minutes) required to mix a batch of material on machines produced by three different manufacturers. To limit the cost of testing, four batches of material were mixed on machines produced by each of the three manufacturers. The times needed to mix the material follow.

(1) Write a multiple regression equation that can be used to analyze the data. 
(2) What are the best estimates of the coefficients in your regression equation?

(3) In terms of the regression equation coefficients, what hypotheses must we test to see whether the mean time to mix a batch of material is the same for all three manufacturers? 
(4)

In the following data on weekly gross revenue, television advertising, and newspaper advertising for Showtime Movie Theaters.

The output is shown below：
The regression equation is
Revenue = 83.2 + 2.29TVAdv +1.30NewsAdv

(1) Find an estimated regression equation relating weekly gross revenue to television and newspaper advertising. 
(2) Check for any outliers in these data. What are your conclusions? 
(3) Interpret the coefficient in the estimated regression equation. 
(4) What is the estimate of the weekly gross revenue for a week when NT$3500 is spent on television advertising and NT$1800 is spent on newspaper advertising?

The Transactional Records Access Clearinghouse at reported data showing the odds of an Internal Revenue Service audit. The following table shows the average adjusted gross income reported and the percent of the returns that were audited for 20 selected IRS districts.

(1) Develop the estimated regression equation that could be used to predict the percent audited given the average adjusted gross income reported. 
(2) At the .05 level of significance, determine whether the adjusted gross income and the percent audited are related. 
(3) Did the estimated regression equation provide a good fit? Explain. 
(4) Use the estimated regression equation developed in part (1) to calculate a 95% confidence interval for the expected percent audited for districts with an average adjusted gross income of $35,000.

(1) Assume that the following output show the daily consumption of the average individual foreign tourists for 30 professions in three sectors: professionals, services and manufacturing (Report on Visitors Expenditure and Trends in Taiwan:2012). Use α = .05 to test for any significant difference in the average of consumption among the three sectors.
The EXCEL output is shown below:
Analysis of Variance

(2) Each month Internet Magazine accesses more than 100 Internet service providers (ISPs) in order to check the availability of the ISP and test the speed of the connection by measuring the time (seconds) it takes to download a number of popular Web pages. The following data show the download time for 22 free ISPs for Web sites located in the United Kingdom, United States, and Europe (Internet Magazine, January 2000). At α = .05 , is there a significant difference in the mean download time for Web sites located in the United Kingdom, United States, and Europe? (5%) The output for these data is shown below:

A company that franchises coffee houses conducted taste tests for a new coffee product. Four blends were prepared, then randomly chosen individuals were asked to taste the blends and state which one they liked best. Results of the taste test for 100 individuals are given.

(1) Define the experiment being conducted. How many times was it repeated? 
(2) Prior to conducting the experiment, it is reasonable to assume preferences for the four blends are equal. What probabilities would you assign to the experimental outcomes prior to conducting the taste test? What method did you use? 
(3) After conducting the taste test, what probabilities would you assign to the experimental outcomes? What method did you use?

The following table shows the percent frequency distributions of job satisfaction scores for a sample of information systems (IS) senior executives and IS middle managers. The scores range from a low of 1 (very dissatisfied) to a high of 5 (very satisfied).

(1) Develop a probability distribution for the job satisfaction score of a senior executive.
(2) Develop a probability distribution for the job satisfaction score of a middle manager.
(3) What is the probability a senior executive will report a job satisfaction score of 4 or 5?
(4) What is the probability a middle manager is very satisfied? 
(5) Compare the overall job satisfaction of senior executives and middle managers.