ASSIGNMENTS

10/20/2008 Change: Assignment 3 clarification

11/19/2008 Change: Assignment 4 clarification for Case 2

The purpose of the homework assignment is to encourage further practice for the topics covered in our book but not covered in class (due to time constraints) and to give you the opportunity to work on more comprehensive exercises than those covered in the book.

Assignment Submitting Standards:

1. All assignments are due at the beginning of the class period.

2. Late assignments will NOT be accepted.

3. All assignments should be printed and stapled together with the cover letter statement (click for sample) on the top.

ASSIGNMENT 1 [top]

Case Problem 1

Fast Food Drive Thru

Thirty fast-food restaurants including Wendy's, McDonald's, and Burger King were visited during the summer of 2000 (The Cincinnati Enquirer, July 9, 2000). During each visit, the customer went to the drive-through and ordered a basic meal such as a "combo" meal or a sandwich, fries, and a shake. The time between pulling up to the menu board and receiving the filled order was recorded (data file FastFood.xls).

Managerial Report

1. Provide a point estimate of the population mean drive-through time at fast-food restaurants.
2. At 95% confidence, what is the margin of error?
3. What is the 90% confidence interval estimation of the population mean?
4. Discuss skewness that may be present in this population. What suggestions would you make for a repeat of this study, in regards to the sample size?

Case Problem 2

Quality Associates, Inc.

Quality Associates, Inc. is a consulting firm which advices its clients about sampling and statistical procedures that can be sued to control their manufacturing processes. In one particular application, a client gave Quality Associates a sample of 800 observations taken during a time in which the client's process was operating satisfactory. The sample standard deviation for this data was 0.21.; hence, with so much data, the population standard deviation was assumed to be 0.21. Quality Associates then suggested that random samples of size 30 be taken periodically to monitor the process on an ongoing basis. By analyzing the new samples, the client could quickly learn whether the process was operating satisfactorily. When the process was not operating satisfactorily, corrective actions could be taken to eliminate the problem. The design specification indicated that the mean for the process should be 12. The hypothesis test suggested by Quality Associates is as follows:

•     Ho: m = 12

•     Ha: NOT m = 12

Corrective action should be taken any time Ho is rejected (data file QualityAssociates.sf6).

Managerial Report

1. Conduct a hypothesis test for each sample at the 0.01 level of significance and determine what action, if any, should be taken.
2. Compute the standard deviation for each of the samples. Does the assumption of 0.21 for the population standard deviation appear reasonable?
3. Compute limits to the sample mean x bar around m=12 such that, as long as a new sample mean is within those limits, the process will be considered to be operating satisfactorily. If x bar is below or above these limits, corrective action will be taken.
4. Discuss the implications of changing the level of significance to a larger value. What mistake or error could increase if the level of significance is increased?

ASSIGNMENT 2  [top]

Case Problem 1

Piston Co.

An automotive industry supplier produces pistons for several models of automotives. Twenty samples, each consisting of 200 pistons, were selected when the process was known to be operating correctly. The number of defective pistons found in the sample are shown below:

 8 10 6 4 5 7 8 12 8 15 14 10 10 7 5 8 6 10 4 10

Managerial Report

Assume that these data were collected when the manufacturing process was believed to be in control develop:
1. A Time Series Plot
2. Runs Test
3. Test for Normality
4. What is an estimate of the proportion defective for the piston manufacturing process when it is in control?
5. Compute the upper and lower control limits for an np chart.
6. Interpret the results and discuss your findings.

Case Problem 2

The Good Earth Co.

The Good Earth Company produces the GECF12 fertilizer for orange trees. Good Earth, periodically tests its fertilizer bags for magnesium content. To study and control the manufacturing process, 20 samples, each containing three bags of fertilizer  were chosen from different shifts over several days of operation and the magnesium content was recorded (data can be found in the Fertilizer.xls file):

Managerial Report

Assume that these data were collected when the manufacturing process was believed to be in control develop:
1. R and x-bar Control Charts
2. Interpret the results and discuss your findings

ASSIGNMENT 3  [top]

Case Problem 1

Oil Analysis

West Texas Intermediate (WTI), also known as Texas Light Sweet, is a type of crude oil used as a benchmark in oil pricing and the underlying commodity of New York Mercantile Exchange's oil futures contracts. This oil type is often referenced in North American news reports about oil prices, alongside North Sea Brent Crude. You are investigating the relationship between the price of WTI crude oil and the price of US stocks. Here is what I want you to do:

1. Select one stock from the S& P 500 index (see a list here) that you believe that there is a STRONG relationship between the stock price and the price of WTI crude oil (positive or negative).

2. Select one stock from the S& P 500 index (see a list here) that you believe that there is NO relationship between the stock price and the price of WTI crude oil.

3. For each one of your 2 stocks:

3.1 Find the daily closing prices from January thru April by using

3.2 Find the daily closing prices for the WTI oil for each of the corresponding closing prices of your stocks using the OilPrices.xls (January thru April).

3.3 Create a spreadsheet which shows the Date, Stock Closing Price, and WTI Oil price (only 3 columns) for your 4 months of data. Use the data from this spreadsheet to produce the managerial report below.

3.4 Please note that you do not have to calculate the Rate of Return of your selected stocks or the Oil prices. Also, if there is no daily value for the price of oil, use the next period's observation.

Managerial Report

For each one of your stocks:

1. Develop a least-squares estimated regression line to determine the relationship between the WTI price and the price of your selected stock.
2. Compute the coefficient of determination and explain its meaning.
3. Are x and y related? Why?
4. Compute the correlation coefficient between the stock price and the price of WTI crude.
5. Perform a t or F test and determine if the stock price and WTI crude are related.
6. Develop a 95% confidence interval for estimating the price of stock when the crude price is  \$ 124.31.

Case Problem 2

Oil Beta

Create a simple linear regression analysis to investigate the relationship between the price of Devon Energy Corporation and the price of WTI oil in the month of May of 2008 (one month only). Use the OilPrices.xls and find the closing prices of DVN using http://finance.yahoo.com/q?s=dvn. For your analysis, develop an oil coefficient (Oil Beta) by examining the Rate of Return for Oil and the Rate of Return of the Devon Energy Corporation stock (please look at the stock beta exercise we performed in class) and investigate their relationship.

Managerial Report

Please note that this question is open-ended. You will collect/determine your data, decide which statistics are relevant in your analysis, and interpret your findings . I expect your analysis to cover both the estimation and diagnostic phases.

ASSIGNMENT 4  [top]

Case Problem 1

Fuel Economy Guide

The U.S. Department of Energy’s Fuel Economy Guide provides fuel efficiency data for cars and trucks (www.fueleconomy.gov). The column labeled Drive identifies 2 Wheel Drive (2WD) or 4 Wheel Drive (4WD). The column labeled Displacement shows the engine’s displacement in litters (partial data shown below). Complete data set is in the FuelEcon.xls file.

 Truck Name Drive Displacement Cylinders Transmission CityMPG 1 C1500 SILVERADO 2WD 4.3 6 Auto 15 2 C1500 SILVERADO 2WD 4.3 6 Manual 15 3 C1500 SILVERADO 2WD 4.8 8 Auto 15 4 C1500 SILVERADO 2WD 4.8 8 Manual 16 5 C1500 SILVERADO 2WD 5.3 8 Auto 11 6 C1500 SILVERADO 2WD 5.3 8 Auto 15 7 C1500 SILVERADO 2WD 5.3 8 Auto 15 8 SSR PICKUP 2WD 5.3 8 Auto 15 9 CHEVY C2500 SILVERADO 2WD 6 8 Auto 10 10 CHEVY C2500 SILVERADO 2WD 6 8 Auto 10 11 C1500 SIERRA 2WD 4.3 6 Auto 16 12 C1500 SIERRA 2WD 4.3 6 Manual 15

Managerial Report

1. Develop an estimated regression equation that can be used to predict the fuel efficiency for city driving given the engine’s displacement. Test for significance using alpha=0.05.

2. Consider the addition of dummy variable Drive4, where the value of Drive4 is 0 if the truck has 2 wheel drive and 1 if the truck has four-wheel drive. Develop the estimated regression equation that can be used to predict the fuel efficiency for city driving given the engine’s displacement and Drive4.

3. Use alpha=0.05 to determine if the dummy variable added above is significant.

4. Consider the addition of the dummy variable EightCyl, where the value of EightCyl is 0 if the truck’s engine has 6 cylinders and 1 if it has eight cylinders. Develop the estimated regression equation that can be used to predict the fuel efficiency for city driving given the engine’s displacement, the dummy variables Drive4 and EightCyl.

5. For the estimated regression equation developed in question 4, test for overall significance and individual significance using alpha=0.05.

Case Problem 2

Transportation Index

The NASDAQ Transportation Index contains securities of NASDAQ-listed companies classified according to the Industry Classification Benchmark as Industrial Transportation and Airlines. They include delivery services, marine transportation, railroads, transportation services, trucking, and airlines. I believe that the monthly retails sales in the U.S. can be partially explained by the Transportation Activity as measured by the Transportation Index. Use the TranIndex.xls data to study the effect of the Transportation Index on the monthly retail sales (data is fictitious).

Managerial Report

Use the methods presented in chapters 15, 16, and especially the Intervention Analysis Discussion to explore the possible relationship between the Retails Sales and the Transportation Index variables. Present a summary of your analysis, including key statistical results, conclusions, and recommendations, in a managerial report. Include any appropriate computer output in your analysis.

ASSIGNMENT 5  [top]

Case Problem 1

Compensation for Sales Professionals

Suppose that a local chapter of sales professionals in Sacramento contacted a survey of its membership to study the relationship, if any, between the years of experience and salary for individuals employed in inside and outside sales positions. A complete set of data is available on the SalesSalary.xls

Managerial Report

1. Use analysis of variance to test for any significant differences due to position. Use alpha=0.05 and, for now, ignore the effects of years of experience.

2. Use analysis of variance to test for any significant differences due to years of experience. Use alpha=0.05 and, for now, ignore the effects of position.

3. Use analysis of variance to test for any significant differences due to position and years of experience. Use alpha=0.05.

4. Present a summary of your analysis, including key statistical results, conclusions, and recommendations, in a managerial report. Include any appropriate computer output in your analysis.

Case Problem 2

Forecasting Food and Beverage Sales

The Vintage Restaurant just completed its third year of operation. Karen, the restaurant owner, needs to develop a system that will enable her to forecast food and beverage sales by month for up to one year in advance. The restaurant's sales in the three years of operation can be found in the Vintage.xls file.

Managerial Report

1. Create a graph of the time series.

2. An analysis of the seasonality of the data.

3. A forecast of sales for January thru December of the fourth year.

4. A comparison of 5 forecasting models. Which one is more appropriate? Why?

5. Recommendations as to when the system that you develop should be updated to account for new sales data.

6. Present a summary of your analysis, including key statistical results, conclusions, and recommendations, in a managerial report. Include any appropriate computer output in your analysis.