Assignment: QUAN METHODS
Part 1
Any documents needed to complete the assignment questions are attached below.
1. To ensure a successful test marketing of its OmniPower energy bars, the OmniFoods marketing department has contracted with In-Store Placements Group (ISPG), a merchandising consultancy. ISPG will work with the grocery store chain that is conducting the test-market study. Using the same 34-store sample used in the test-market study, ISPG claims that the choice of shelf location and the presence of in-store OmniPower coupon dispensers both increase sales of the energy bars. Open Omni_ISPGMemo.pdf to review the ISPG claims and supporting data.
Then answer the following questions:
a. Are the supporting data consistent with ISPG's claims? Perform an appropriate statistical analysis to confirm (or discredit) the stated relationship between sales and the two independent variables of product shelf location and the presence of in- store OmniPower coupon dispensers.
b. If you were advising OmniFoods, would you recommend using a specific shelf location and in-store coupon dispensers to sell OmniPower bars?
c. What additional data would you advise collecting in order to determine the effectiveness of the sales promotion techniques used by ISPG?
2. Measuring the height of a California redwood tree is a very difficult undertaking because these trees grow to heights of over 300 feet. People familiar with these trees understand that the height of a California redwood tree is related to other characteristics of the tree, including the diameter of the tree at the breast height of a person. The data in represent the height (in feet) and diameter (in inches) at the breast height of a person for a sample of 21 California redwood trees.
a. Assuming a linear relationship, use the least-squares method to compute the regression coefficients b 0 and b 1. State the regression equation that predicts the height of a tree based on the tree's diameter at breast height of a person.
b. Interpret the meaning of the slope in this equation.
c. Predict the height for a tree that has a breast height diameter of 25 inches.
d. Interpret the meaning of the coefficient of determination in this problem.
e. Perform a residual analysis on the results and determine the adequacy of the model.
f. Determine whether there is a significant relationship between the height of redwood trees and the breast height diameter at the 0.05 level of significance.
g. Construct a 95% confidence interval estimate of the population slope between the height of the redwood trees and breast height diameter.
3. Leasing agents from the Triangle Mall Management Corporation have suggested that Sunflowers consider several locations in some of Triangle's newly renovated lifestyle malls that cater to shoppers with higher-than-mean disposable income. Although the locations are smaller than the typical Sunflowers location, the leasing agents argue that higher-than-mean disposable income in the surrounding community is a better predictor than store size of higher sales. The leasing agents maintain that sample data from 14 Sunflowers stores prove that this is true.
Open Triangle_Sunflower.pdf and review the leasing agents' proposal and supporting documents.
Then answer the following questions:
a. Should mean disposable income be used to predict sales based on the sample of 14 Sunflowers stores?
b. Should the management of Sunflowers accept the claims of Triangle's leasing agents? Why or why not?
c. Is it possible that the mean disposable income of the surrounding area is not an important factor in leasing new locations? Explain.
d. Are there any other factors not mentioned by the leasing agents that might be relevant to the store leasing decision?
4. Professional basketball has truly become a sport that generates interest among fans around the world. More and more players come from outside the United States to play in the National Basketball Association (NBA). You want to develop a regression model to predict the number of wins achieved by each NBA team, based on field goal (shots made) percentage for the team and for the opponent. The data are stored in NBA2011.xls.
a. State the multiple regression equation.
b. Interpret the meaning of the slopes in this equation.
c. Predict the number of wins for a team that has a field goal percentage of 45% and an opponent field goal percentage of 44%.
d. Perform a residual analysis on your results and determine whether the regression assumptions are valid.
e. Is there a significant relationship between number of wins and the two independent variables (field goal percentage for the team and for the opponent) at the 0.05 level of significance?
f. Determine the p-value in (e) and interpret its meaning.
g. Interpret the meaning of the coefficient of multiple determination in this problem.
h. Determine the adjusted r2
i. At the 0.05 level of significance, determine whether each independent variable makes a significant contribution to the regression model. Indicate the most appropriate regression model for this set of data.
j. Determine the p-values in (i) and interpret their meaning.
5. A sample of 30 recently sold single-family houses in a small city is selected. Develop a model to predict the selling price (in thousands of dollars), using the assessed value (in thousands of dollars) as well as time (in months since reassessment). The houses in the city had been reassessed at full value one year prior to the study. The results are stored in House1.xls.
a. State the multiple regression equation.
b. Interpret the meaning of the slopes in this equation.
c. Predict the selling price for a house that has an assessed value of $170,000 and was sold 12 months after reassessment.
d. Perform a residual analysis on your results and deter-mine whether the regression assumptions are valid.
e. Determine whether there is a significant relationship be-tween selling price and the two independent variables (assessed value and time period) at the 0.05 level of significance.
f. Determine the p-value in (e) and interpret its meaning.
g. Interpret the meaning of the coefficient of multiple determination in this problem.
h. Determine the adjusted
i. At the 0.05 level of significance, determine whether each independent variable makes a significant contribution to the regression model. Indicate the most appropriate regression model for this set of data.
j. Determine the p-values in (i) and interpret their meaning.
k. Construct a 95% confidence interval estimate of the population slope between selling price and assessed value.
Part 2
Any documents needed to complete the assignment questions are attached below.
1. The manufacturer of Boston and Vermont asphalt shingles constructed control charts and analyzed several quality characteristics. One characteristic of interest is the strength of the sealant on the shingle. During each day of production, three shingles are tested for their sealant strength. (Thus, a subgroup is operationally defined as one day of production, and the sample size for each subgroup is 3.) Separate pieces are cut from the upper and lower portions of a shingle and then reassembled to simulate shingles on a roof. A timed heating process is used to simulate the sealing process. The sealed shingle pieces are pulled apart, and the amount of force (in pounds) required to break the sealant bond is measured and recorded. This variable is called the sealant strength.
The file contains sealant strength measurements on 25 days of production for Boston shingles and 19 days for Vermont shingles. For the 25 days of production for Boston shingles,
a. construct a control chart for the range.
b. construct a control chart for the mean.
c. is the process in control?
d. Repeat (a) through (c), using the 19 production days for Vermont shingles.
2. The AMS technical services team has embarked on a quality improvement effort. Its first project relates to maintaining the target upload speed for its Internet service subscribers. Upload speeds are measured on a device that records the results on a standard scale in which the target value is 1.0. Each day five uploads are randomly selected, and the speed of each upload is measured. The results for 25 days is stored in AMS14.xl
a. Construct the appropriate control charts for these data.
b. Is the process in a state of statistical control? Explain.
c. What should the team recommend as the next step to improve the process?
3. Harnswell Sewing Machine Company
Phase 1: For more than 40 years, the Harnswell Sewing Machine Company has manufactured industrial sewing machines. The company specializes in automated machines called pattern tackers that sew repetitive patterns on such mass-produced products as shoes, garments, and seat belts. Aside from the sales of machines, the company sells machine parts. Because the company's products have a reputation for being superior, Harnswell is able to command a price premium for its product line.
Recently, the operations manager, Natalie York, purchased several books related to quality. After reading them, she considered the feasibility of beginning a quality program at the company. At the current time, the company has no formal quality program. Parts are 100% inspected at the time of shipping to a customer or installation in a machine, yet Natalie has always wondered why inventory of certain parts (in particular, the half-inch cam rollers) invariably falls short before a full year lapses, even though 7,000 pieces have been produced for a demand of 5,000 pieces per year.
After a great deal of reflection and with some apprehension, Natalie has decided that she will approach John Harnswell, the owner of the company, about the possibility of beginning a program to improve quality in the company, starting with a trial project in the machine parts area. As she is walking to Mr. Harnswell's office for the meeting, she has second thoughts about whether this is such a good idea. After all, just last month, Mr. Harnswell told her, "Why do you need to go to graduate school for your master's degree in business? That is a waste of your time and will not be of any value to the Harnswell Company. All those professors are just up in their ivory towers and don't know a thing about running a business, like I do."
As she enters his office, Mr. Harnswell invites Natalie to sit down across from him. "Well, what do you have on your mind this morning?" Mr. Harnswell asks her in an inquisitive tone. She begins by starting to talk about the books that she has just completed reading and about how she has some interesting ideas for making production even better than it is now and improving profits. Before she can finish, Mr. Harnswell has started to answer: "Look, everything has been fine since I started this company in 1968. I have built this company up from nothing to one that employs more than 100 people. Why do you want to make waves? Remember, if it ain't broke, don't fix it." With that, he ushers her from his office with the admonishment of, "What am I going to do with you if you keep coming up with these ridiculous ideas?"
a. Based on what you have read, which of Deming's 14 points of management are most lacking at the Harnswell Sewing Machine Company? Explain.
b. What changes, if any, do you think that Natalie York might be able to institute in the company? Explain.
Phase 2: Natalie slowly walks down the hall after leaving Mr. Harnswell's office, feeling rather downcast. He just won't listen to anyone, she thinks. As she walks, Jim Murante, the shop foreman, comes up beside her. "So," he says, "did you really think that he would listen to you? I've been here more than 25 years. The only way he listens is if he is shown something that worked after it has already been done. Let's see what we can plan together."
Natalie and Jim decide to begin by investigating the production of the cam rollers, which are precision-ground parts. The last part of the production process involves the grinding of the outer diameter. After grinding, the part mates with the cam groove of the particular sewing pattern. The half-inch rollers technically have an engineering specification for the outer diameter of the roller of 0.5075 inch (the specifications are actually metric, but in factory floor jargon, they are referred to as half-inch), plus a tolerable error of 0.0003 inch on the lower side. Thus, the outer diameter is allowed to be between 0.5072 and 0.5075 inch. Anything larger is reclassified into a different and less costly category, and anything smaller is unusable for anything other than scrap.
The grinding of the cam roller is done on a single machine with a single tool setup and no change in the grinding wheel after initial setup. The operation is done by Dave Martin, the head machinist, who has 30 years of experience in the trade and specific experience producing the cam roller part. Because production occurs in batches, Natalie and Jim sample five parts produced from each batch. Table below presents data collected over 30 batches (stored in Harnswell).
a. Is the process in control? Why?
b. What recommendations do you have for improving the process?
Phase 3: Natalie examines the X and R charts developed from the data stored in Harnswell.xls from Phase 2. The R chart indicates that the process is in control, but the chart X t reveals that the mean for batch 17 is outside the LCL. This immediately gives her cause for concern because low values for the roller diameter could mean that parts have to be scrapped. Natalie goes to see Jim Murante, the shop foreman, to try to find out what had happened to batch 17. Jim looks up the production records to determine when this batch was produced. "Aha!" he exclaims. "I think I've got the answer! This batch was produced on that really-cold morning we had last month. I've been after Mr. Harnswell for a long time to let us install an automatic thermostat here in the shop so that the place doesn't feel so cold when we get here in the morning. All he ever tells me is that people aren't as tough as they used to be."
Natalie is almost in shock. She realizes that what happened is that, rather than standing idle until the environment and the equipment warmed to acceptable temperatures, the machinist opted to manufacture parts that might have to be scrapped. In fact, Natalie recalls that a major problem occurred on that same day, when several other expensive parts had to be scrapped. Natalie says to Jim, "We just have to do something. We can't let this go on now that we know what problems it is potentially causing." Natalie and Jim decide to take enough money out of petty cash to get the thermostat without having to fill out a requisition requiring Mr. Harnswell's signature. They install the thermostat and set the heating control so that the heat turns on a half hour before the shop opens each morning.
a. What should Natalie do now concerning the cam roller data? Explain.
b. Explain how the actions of Natalie and Jim to avoid this particular problem in the future have resulted in quality improvement.
PHASE 4: Because corrective action was taken to eliminate the special cause of variation, Natalie removes the data for batch 17 from the analysis. The control charts for the remaining days indicate a stable system, with only common causes of variation operating on the system. Then, Natalie and Jim sit down with Dave Martin and several other machinists to try to determine all the possible causes for the existence of oversized and scrapped rollers. Natalie is still troubled by the data. After all, she wants to find out whether the process is giving oversizes (which are downgraded) and undersizes (which are scrapped). She thinks about which tables and charts might be most helpful.
a. Construct a frequency distribution and a stem-and-leaf display of the cam roller diameters. Which do you prefer in this situation?
b. Based on your results in (a), construct all appropriate charts of the cam roller diameters.
c. Write a report, expressing your conclusions concerning the cam roller diameters. Be sure to discuss the diameters as they relate to the specifications.
PHASE 5: Natalie notices immediately that the overall mean diameter with batch 17 eliminated is 0.507527, which is higher than the specification value. Thus, the mean diameter of the rollers produced is so high that many will be downgraded in value. In fact, 55 of the 150 rollers sampled (36.67%) are above the specification value. If this percentage is extrapolated to the full year's production, 36.67% of the 7,000 pieces manufactured, or 2,567, could not be sold as half-inch rollers, leaving only 4,433 available for sale. "No wonder we often have shortages that require costly emergency runs," she thinks. She also notes that not one diameter is below the lower specification of 0.5072, so not one of the rollers had to be scrapped.
Natalie realizes that there has to be a reason for all this. Along with Jim Murante, she decides to show the results to Dave Martin, the head machinist. Dave says that the results don't surprise him that much. "You know," he says, "there is only 0.0003 inch variation in diameter that I'm allowed. If I aim for exactly halfway between 0.5072 and 0.5075, I'm afraid that I'll make a lot of short pieces that will have to be scrapped. I know from way back when I first started here that Mr. Harnswell and everybody else will come down on my head if they start seeing too many of those scraps. I figure that if I aim at 0.5075, the worst thing that will happen will be a bunch of downgrades, but I won't make any pieces that have to be scrapped."
a. What approach do you think the machinist should take in terms of the diameter he should aim for? Explain.
b. What do you think that Natalie should do next? Explain.
4. Use the Random Number Table E.1 from Page 544 of the textbook to simulate the selection of different-colored balls from an urn, as follows:
a. Start in the row corresponding to the day of the month in which you were born plus the last two digits of the year in which you were born. For example, if you were born October 3, 1990, you would start in row 93 (3 + 90). If your total exceeds 100, subtract 100 from the total.
b. Select two-digit random numbers.
c. If you select a random number from 00 to 94, consider the ball to be white; if the random number is from 95 to 99, consider the ball to be red.
Each student is to select 100 two-digit random numbers and report the number of "red balls" in the sample. Construct a control chart for the proportion of red balls.
d. What conclusions can you draw about the system of selecting red balls?
e. Are all the students part of the system?
f. Is anyone outside the system? If so, what explanation can you give for someone who has too many red balls?
g. If a bonus were paid to the top 10% of the students (the 10% with the fewest red balls), what effect would that have on the rest of the students? Discuss.
5. As chief operating officer of a local community hospital, you have just returned from a three-day seminar on quality and productivity. It is your intention to implement many of the ideas that you learned at the seminar. You have decided to construct control charts for the upcoming month for the proportion of rework in the laboratory (based on 1,000 daily samples) and time (in hours) between receipt of a specimen at the laboratory and completion of the work (based on a subgroup of 10 specimens per day). The data collected are summarized and stored in HospAdm.xls. You are to make a presentation to the chief executive officer of the hospital and the board of directors. Prepare a report that summarizes the conclusions drawn from analyzing control charts for these variables. In addition, recommend additional variables to measure and monitor by using control charts.
Format your assignment according to the following formatting requirements:
1. The answer should be typed, double spaced, using Times New Roman font (size 12), with one-inch margins on all sides.
2. The response also includes a cover page containing the title of the assignment, the student's name, the course title, and the date. The cover page is not included in the required page length.
3. Also include a reference page. The Citations and references should follow APA format. The reference page is not included in the required page length.