Central Ohio Technical College Data Driven Decision Making Paper
please use excel to answer these questions, PLEASE READ ALL DIRECTIONS as there are a few different requirements and SHOW ALL WORK FOR EACH QUESTION WITH EXCELPlease make sure you put your name in the space provided at the top right corner of this page.Please insure that your copy of the exam has 8 numbered pages and 12 questions (and two EXTRA-CREDIT questions).You may use your textbook, computer, and notes. You should do all the work on your own and not get any help from others (this includes tutors). Integrate, i.e., cut & paste, computer printouts (as part of the response to the questions) for any questions you use the computer analysis results.For the normal distribution problems #8 and #9, draw appropriate pictures and mark relevant points on the picture by using the Minitab “graph à probability distribution plot” function (you could also do this by drawing the picture on paper, scanning it, and incorporating into your answer).Please turn-in this exam as an electronic (soft) copy. You should type in your answers on this document and turn it in for grading. Please name the Word file as you have done for all submissions in this class. GRADE SUMMARYProblems: Partial44Problems: Complete24Short essays32Extra-Credit10 Total110GOOD LUCKFor your use with Word, I am providing some symbols we have used in class. You may cut-and-paste these symbols as and when you need them on this.= < > ≥ ≤ ≠ µ σ σσ2 S S2H0: H1: a PROBLEMS --PARTIALFor the following three business situations please identify whether the probability distribution to be used to model the situation is Binomial, Poisson, or some other distribution (you do not need to identify this if it is not Binomial or Poisson distribution, just state that it is an unknown distribution) and for each situation justify your choice of the probability distribution by listing the requirements of the distribution and how they are met. (You are not required to solve these problems) (2 + 2 points)Any profit-maximizing firm would like a larger share of the market. The advertising campaign in different communications media is the most effective method to reach the consumers. Chuck Atwood, Optico Corporation’s sales manager, recently concluded a six-month advertising campaign which featured a series of ads in major business periodicals. The firm’s advertising agency assured Optico management that 60% of the purchasing agents in the target industries would be aware of the campaign. At a recent sales convention, only 4 of the 10 purchasing agents whom Chuck Atwood questioned could remember seeing any of the ads. Should Optico undertake a more detailed (and expensive) study of the advertising agency’s claim? Why?Pat Lowe, general manager of Chicago Foundries, is facing a difficult situation. Her plant is currently operating at 60 percent of optimal capacity and is losing money. She has submitted bids on two government contracts, either of which would bring the plant up to capacity. However, if she were to receive both, she would have to subcontract one of them and would be no better off than she currently is. Lowe recently received an invitation to bid on another government contract of the same nature and magnitude as the two she currently has bids on. She is unsure whether she should bid. She would prefer to operate at 60 percent capacity than to receive all three bids. Past experience has convinced her that she has received contracts of this nature 20 percent of the time. Advise Ms. Lowe.Telephone sales operators make on the average 1 call every 10 minutes. Recently, operators have become upset with their working conditions and you wonder if they are slowing down to retaliate. You observe one operator who has made no calls in the past 50 minutes. Assume that the average of 1 call every 10 minutes has not changed. What is the probability that no calls would have been made in the past 50 minutes?For the next four problems, just do the following: (You are not required to solve these problems)A.Set up Null (H0) and alternate (H1) hypotheses (i.e., Step 1) in business terms (i.e., in plain English). (2 points)B.Set up Null (H0) and alternate (H1) hypotheses (i.e., Step 1) in statistical terms. (2 points)C.In the context of the problem, please specify what kind of conclusion will lead to type I error and discuss the implications of making this type of error (i.e., who will it impact and how). (2 + 2 points)The Better Business Bureau has received several complaints that a flour company is underfilling their five pound bags of flour. The Bureau randomly selects 750 bags of flour and determines the weight of each bag. The sample average weight of the bags is 4.80 pounds with a standard deviation of .15 pounds. Is there evidence at the .01 level of significance that the bags are underfilled? A. H0 : H1 :B. H0 : H1 :C.5.The director of the IRS has been flooded with complaints that people must wait for at least 45 minutes before seeing an IRS representative. To determine the validity of these complaints, the IRS randomly selects 400 people entering IRS offices across the country and records the times which they must wait before seeing an IRS representative. The average waiting time for the sample is 55 minutes with a standard deviation of 15 minutes. Are the complaints substantiated by the data? Use a significance level, α, of .10.A. H0 : H1 :B. H0 : H1 :C. A 1990 Survey showed that the average check at Perkins family restaurant is $4.70. The Perkins company wants to know if this figure is too high for 1997. The Perkins company takes a random sample of 54 checks from the restaurants across the country and determines that the sample average check is $4.62. The sample standard deviation of the checks is $0.86. Using a = .05, test to determine whether the Perkins, restaurant check average is significantly lower than $4.70.A. H0 : H1 :B. H0 : H1 :C. To protect U. S. steel producers against competition from low-priced foreign imports, theGovernment has adopted a trigger price mechanism. If steel imports enter this country at less than the minimum or trigger price (based on the cost of production in Japan, which has the world's most efficient steel factories), an investigation into the illegal dumping of cheap steel in the United States by foreign countries is launched. Last year, the average trigger price was set at $358.31 per ton. This year, a random sample of n = 40 was selected, and the trigger price on each of the days was recorded. The data are summarized as follows: Sample mean = $330.88 S = $106.1Does the sample evidence indicate a need for an investigation of illegal dumping?A. H0 : H1 :B. H0 : H1 :C. PROBLEMS – COMPLETE8.A well-known brand of size D batteries has a lifetime that is normally distributed with a mean of 105 hours and a standard deviation of 20 hours. A. What proportion of the batteries has a lifetime of less than 85 hours? (4 points) B. If a person buys 1 battery of this type, what would be the probability that its lifetime would be between 75 and 90 hours? (4 points) 9A A personnel researcher has designed a questionnaire and she would like to estimate the average time to complete the questionnaire. Suppose she samples 100 employees and finds that the mean time to take the test is 27 minutes with a standard deviation of 4 minutes. Construct a 90% confidence interval for the mean time to complete the questionnaire. (6 points) Also, write a short memorandum about the findings to the human resources director of your company summarizing the methodology, findings, results and conclusions. (4 points) – Use Minitab for this analysis.9B. For the problem in part A, the human resources director wants to know whether these is sufficient sample evidence to conclude that the average time to complete the questionnaire is not 27 minutes. Set up the hypotheses (in statistical terms) and, based only on the confidence interval you have constructed in part A, what would you conclude regarding the hypotheses? (6 points) H0 : H1 :Conclusion:ESSAYS (Please double space your work)Management researchers are interested in understanding factors that are related to success of managers in for-profit businesses. You have been hired as a consultant to assist the researchers. As you start your work, develop a plan that addresses the following (page limit: 2 pages):a)What is your clear definition of the problem? i.e., what is it that you would like to show with evidence from data and analysis? (4 points)b)What data would you collect? Identify and specify the variables (so that they can be measured), list them including type and level, and specify why each variable is useful (or needed) for the study. List a few (made-up) values for each variable. Be very specific and to the point. (6 points)c)Present a plan, for collecting the data specified above, in the form of a series of specific instructions for someone else that would actually collect the data for you. (6 points)d)Provide a justification for your plan as it pertains to the quality of the variables that you selected (i.e., explain why you believe that the variables are the best ones to measure to address the issue raised in the study). You may contrast your variables with others (or other ways to measure the same variables) of lesser quality to make your point that yours are the best. (4 points)Write a short tutorial describing, in your own words, "hypothesis testing" to a manager who is not very knowledgeable in business statistics. Do not list the steps or describe the statistical analysis, but describe it as a technique to solve business problems. Use an example problem/situation to illustrate your points. (Page limit: ½ page) (8 points)undefinedSuppose an investment broker’s claim is stated in the hypotheses as: H0: My clients earn an average return of at most 10% per year on their investments. H1: My clients earn an average return of more than 10% per year on their investments.What is the type I error here? What are the implications of this error? Who is affected and why? Explain. (4 points)
