You were recently hired as the vice president of marketing for the ABC company. The CEO specifically chose you because of your statistics background, which you earned during your undergraduate degree. In the past, many of the firm’s department heads and senior managers seemed to make decisions quickly, and the company frequently suffered as a result. With the firm’s long-term viability at stake, the CEO felt it was crucial that all future significant decisions be made based on rational thought processes and some quantitative analyses. Although much of your work will be in your own marketing department, the CEO also indicated that the production manager in the factory needed some assistance in controlling his manufacturing processes, and you offered to assist in teaching him how to use statistical process control. The CEO asked you to put together a report consisting of the following sections. Some of the report will be actual data analysis, some will be on sampling methods, and a section will be of value to the vice president of production. Section A: The company is thinking of launching a new product line and wishes to assess the likely response from regular customers. A survey has been taken showing the following response to a question dealing with customers’ satisfaction with the existing product line. On a scale of 1(very dissatisfied) to 5 (very satisfied), the responses from 300 customers were the following: Score of 5: 120 or 40% of sample Score of 4: 45 or 15% of sample Score of 3: 45 or 15% of sample Score of 2: 60 or 20% of sample Score of 1: 30 or 10% of sample Total sample: 300 Regardless of this sample, you feel that the actual satisfaction scores of the total target market are normally distributed. Answer the following: What was the data mean or average satisfaction score? What was the mode? What was the median? What was the standard deviation? As a marketing person, which of the statistical results would mean the most to you if you did not know that the population’s results were normally distributed? Why? Would your answer be any different to question 5 if you knew that the population was normally distributed? Why? Section B: Thinking back to your statistics courses, you noticed that the sample size was only 20, and you pulled out some of your old texts to check on what that meant in terms of your interpretation of the results. Assuming the CEO would like to be able to believe the sample’s average satisfaction score is no more than 0.25 of the real target market average satisfaction score, and would like to have a 95% confidence level in the validity of the result, what sample size should you have used in the market research? Assume the population is normally distributed. What is the likely ramification of having too small a sample? You also wonder if there is any correlation between household income and the satisfaction index on the new product, so you extract some more data from the market research, and add it to the table above. Average household income: Score of 5:8 $38,000 Score of 4:3 $50,000 Score of 3:3 $48,000 Score of 2:4 $80,000 Score of 1:2 $85,000 Total sample: 20 Section C: You wonder what the relationship is between customers’ household incomes and their satisfaction with the new product line. Fill out and turn in the Excel spreadsheet showing the data for which you will determine the correlation. What is the correlation coefficient? Is there a strong or weak correlation? Is it positive or negative? What conclusions can you reach about the relationship between household income and customer satisfaction? As the vice president of marketing, what might you now do with this correlation information? Section D: You know from previous experience that the most successful new product launches have prelaunch sample satisfaction scores of 4.0. You want to use statistical analysis and hypothesis testing to determine if, given the sample information that you have, the target market will in fact have a mean of at least 4.0. To properly answer this question, what would be the null hypothesis? What would be the alternative hypothesis? Assuming that you wish to have a 95% confidence interval in your conclusion, what is the value of the t-statistic and the test statistic? What conclusion can you reach based on the test statistic? In your own words, explain what your t-test has just shown. Section E: The CEO also asked you to include in your report a “how to” set of instructions on using statistical process control in a manufacturing process, so you have to add the following to the final section of the report: In layman’s terms, what is statistical process control (SPC)? What information is needed to create an SPC chart? Use the following information to create an actual SPC chart, and then plot the actual sample data points taken during the last 24 hours: Part dimension and tolerance should be 1.0 +/- 0.025. The SPC chart should show UCL, LCL, USL, and LSL lines, plus the sample data from the last 24 hours When the process capability study was done a week ago, and the process was deemed to be capable of producing parts to specification, the results of consecutive samples showed 4 parts at 1.0, 4 parts at 1.01, 2 parts at 0.99, 5 parts at 0.98, and 5 parts at 0.985. Today’s sample of 5 consecutive parts measured out at 1.032, 1.034, 1.0346, and 1.0345. Based on what the chart now looks like, what observation can be made about the process from which the data was collected?
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