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In the Manufacturing database, what is the probability that a randomly selected SIC Code industry is in industry group 13? What is the probability that a randomly selected SIC Code industry has a value of industry shipments of 4 (see Chapter 1 for coding)? What is the probability that a randomly selected SIC Code industry is in industry group 13 and has a value of industry shipments of 2? What is the probability that a randomly selected SIC Code industry is in industry group 13 or has a value of industry shipments of 2? What is the probability that a randomly selected SIC Code industry neither is in industry group 13 nor has a value of industry shipments of 2?Use the Hospital database. Construct a cross-tabulation table for region and for type of control. You should have a 7 × 4 table. Using this table, answer the following questions. (Refer to Chapter 1 for category members.) What is the probability that a randomly selected hospital is in the Midwest if the hospital is known to be for-profit? If the hospital is known to be in the South, what is the probability that it is a government, nonfederal hospital? What is the probability that a hospital is in the Rocky Mountain region or a not-for-profit, nongovernment hospital? What is the probability that a hospital is a for-profit hospital located in California?

Using the manufacturer database, construct a frequency distribution for the variable Number of Production Workers. What does the frequency distribution reveal about the number of production workers?

Using the Consumer Food database, construct a histogram for the variable Annual Food Spending. How is the histogram shaped? Is it high in the middle or high near one or both ends of the data? Is it relatively constant in size across the class (uniform), or does it appear to have no shape? Does it appear to be nearly “normally” distributed?

Construct an ogive for the variable Type in the financial database. The 100 companies in this database are each categorized into one of seven types of companies. These types are listed at the end of Chapter 1. Construct a pie chart of these types and discuss the output. For example, which type is most prevalent in the database and which is the least?

Study the Minitab-produced dot plot of the number of farms per state in the United States shown below. Comment on any observations that you make from the graph. What does this graph tell you about the number of farms per state? The average number of farms per state calculated from the raw data (not given here) and sourced from the U.S. Department of Agriculture is 44,060. Reconcile this number with the dot plot.

According to Bureau of Transportation statistics, the largest five U.S. airlines in scheduled system-wide (domestic and international) enplanements in 2013 (passenger numbers in millions) were: Delta with 120.4, Southwest with 115.3, United with 90.1, American with 86.8 and US Airways with 57.0. Construct a pie chart and a bar graph to depict this information.

What are the mean and the median amounts of new capital expenditures for industries in the Manufacturing database? Comparing the mean and the median for these data, what do these statistics tell you about the data?

1. In several countries of Africa, a common size for a Coke can is 340 milliliters (mL). Because of the variability of bottling machinery, it is likely that every 340-mL bottle of Coca-Cola does not contain exactly 340 milliliters of fluid. Some bottles may contain more fluid and others less. Because of this variation, a production engineer wants to test some of the bottles from a production run to determine how close they are to the 340-mL specification. Suppose the following data are the fill measurements from a random sample of 50 cans. Use the techniques presented in this chapter to describe the sample. Consider measures of central tendency, variability, and skewness. Based on this analysis, how is the bottling process working on this production run?

2. Suppose that at another plant Coca-Cola is filling bottles with 20 ounces of fluid. A lab randomly samples 150 bottles and tests the bottles for fill volume. The descriptive statistics are given in both Minitab and Excel computer output. Write a brief report to supervisors summarizing what this output is saying about the process.

a. Using measures of central tendency including the mean, median, and mode, describe annual food spending and annual household income for the 200 households in the Consumer Food database. Compare the two results by determining approximately.

b. What percentage of annual household income is spend on food?

Using the Financial database, study earnings per share for Type 2 and Type 7 companies (chemical and petrochemical) using statistics. Compute a coefficient of variation for both Type 2 and Type 7. Compare the two coefficients and comment on them.

Using the Hospital database, construct a box-and-whisker plot for births. Thinking about hospitals and birthing facilities, comment on why the box-and-whisker plot looks like it does.

Use the Hospital database. Construct a cross-tabulation table for region and for type of control. You should have a 7 × 4 table. Using this table, answer the following questions. (Refer to Chapter 1 for category members.) What is the probability that a randomly selected hospital is in the Midwest if the hospital is known to be for-profit? If the hospital is known to be in the South, what is the probability that it is a government, nonfederal hospital? What is the probability that a hospital is in the Rocky Mountain region or a not-for-profit, nongovernment hospital? What is the probability that a hospital is a for-profit hospital located in California?

According to Nielsen Media Research, approximately 86% of all U.S. households have High-definition television (HDTV). In addition, 49% of all U.S. households own Digital Video Recorders (DVR). Suppose 40% of all U.S. households have HDTV and have DVR. A U.S. household is randomly selected.

a. What is the probability that the household has HDTV or has DVR?

b. What is the probability that the household does not have HDTV or does have DVR?

c. What is the probability that the household does have HDTV or does not have DVR?

d. What is the probability that the household does not have HDTV or does not have DVR?

International Housewares Association (IHA) reported that 73% of all U.S. households have ceiling fans. In addition, 77% of all U.S. households have an outdoor grill. Suppose 60% of all U.S. households have both a ceiling fan and an outdoor grill. A U.S. household is randomly selected.

a. What is the probability that the household has a ceiling fan or an outdoor grill?

b. What is the probability that the household has neither a ceiling fan nor an outdoor grill?

c. What is the probability that the household does not have a ceiling fan and does have an outdoor grill?

d. What is the probability that the household does have a ceiling fan and does not have an outdoor grill?

Use the Consumer Food database. What proportion of the database households are in the Metro area? Use this as the value of p in a binomial distribution. If you were to randomly select 12 of these households, what is the probability that fewer than 3 would be households in the Metro area? If you were to randomly select 25 of these households, what is the probability that exactly 8 would be in the Metro area?

1. Whole Foods Market has shown steady growth at a time when traditional supermarkets have been flat. This could be attributed to a growing awareness of and demand for more natural foods. According to a study by Mintel in 2006, 30% of consumers have a high level of concern about the safety of the food they eat. Suppose we want to test this figure to determine if consumers have changed since then. Assuming that the 30% figure still holds, what is the probability of randomly sampling 25 consumers and having 12 or more respond that they have a high level of concern about the safety of the food they eat? What would the expected number be? If a researcher actually got 12 or more out of 25 to respond that they have a high level of concern about the safety of the food they eat, what might this mean?

2. Suppose that, on average, in a Whole Foods Market in Dallas, 3.4 customers want to check out every minute. Based on this figure, store management wants to staff checkout lines such that less than 1% of the time demand for checkout cannot be met. In this case, store management would have to staff for what number of customers? Based on the 3.4 customer average per minute, what percentage of the time would the store have 12 or more customers who want to check out in any two-minute period?

3. Suppose a survey is taken of 30 managers of Whole Foods Market stores and it is determined that 17 are at least 40 years old. If another researcher randomly selects 10 of these 30 managers to interview, what is the probability that 3 or fewer are at least 40 years old? Suppose 9 of the 30 surveyed managers are female. What is the probability of randomly selecting 10 managers from the 30 and finding out that 7 of the 10 are female?

Over three decades ago, four businesspeople who had experience in retailing natural foods through food stores believed that there was a demand for a supermarket for natural foods. As a result, in 1980 in Austin, Texas, they founded the first Whole Foods Market store in a building that had around 10,000 square feet and a staff of 19. This store was quite large compared to health food stores at the time. By 1984, the company was successful enough to expand to Houston and Dallas. In 1988, they purchased the Whole Food Company in New Orleans and expanded there. The next year, they moved into the West Coast with a store in Palo Alto, California. Even though the company has built a number of its own stores, much of the company growth has come through mergers and acquisitions, many of which came in the 1990s in such places as North Carolina, Massachusetts, Rhode Island, both Northern and Southern California, and Michigan. After the turn of the century, Whole Foods Market established a presence in Manhattan (NY), followed by a move into Canada and later into the United Kingdom.

Presently, Whole Foods Market has 433 stores including 414 stores in 42 U.S. states and the District of Columbia, 10 stores in Canada, and 9 stores in the United Kingdom. There are over 91,000 team members, many of whom are full-time employees. Existing stores now average 43,000 square feet in size, about four times as large as the original “supermarket”. Whole Foods Market is the eighth largest food and drug store in the United States with over $14 billion in sales last year and ranks 218 on the list of Fortune 500 companies.

Whole Food Markets is the largest retailer of natural and organic foods and prides itself in doing the research necessary to assure customers that offered products are free of artificial flavors, colors, sweeteners, preservatives, or hydrogenated fats. The company attempts to customize each store by stocking it with products that are most in demand in any given community. Whole Foods Market management cares about their employees, and the company has been named by Fortune magazine as one of the “100 Best Companies to Work For” in the United States every year since the list was first compiled 18 years ago. The company attempts to be a good community citizen, and it gives back at least 5% of after-tax profits to the communities in which they operate. In January 2008, Whole Foods Market was the first U.S. supermarket to commit to completely eliminating disposable plastic bags. The Core Values of the company are “Whole Foods, Whole People, and Whole Planet.” The Whole Foods Market searches “for the highest quality, least processed, most flavorful and natural foods possible . . .” The company attempts to “create a respectful workplace where people are treated fairly and are highly motivated to succeed.” In addition, the company is committed to the world around us and protecting the planet.

Use the Hospital database. What is the breakdown between hospitals that are general medical hospitals and those that are psychiatric hospitals in this database of 200 hospitals? In Service, 1 = general medical and 2 = psychiatric. Using these figures and the hypergeometric distribution, determine the probability of randomly selecting 16 hospitals from the database and getting exactly 9 that are psychiatric hospitals. Now, determine the number of hospitals in this database that are for-profit (In Control, 3 = for-profit.) From this number, calculate p, the proportion of hospitals that are for-profit. Using this value of p and the binomial distribution, determine the probability of randomly selecting 30 hospitals and getting exactly 10 that are for-profit.

The Consumer Food database contains a variable, Annual Food Spending, which represents the amount spent per household on food for a year. Calculate the mean and standard deviation for this variable that is approximately normally distributed in this database. Using the mean and standard deviation, calculate the probability that a randomly selected household spends more than $10,000 annually on food. What is the probability that a randomly selected household spends less than $5,000 annually on food? What is the probability that a randomly selected household spends between $8,000 and $11,000 annually on food?

Select the Agribusiness time-series database. Create a histogram graph for onions and for broccoli. Each of these variables is approximately normally distributed. Compute the mean and the standard deviation for each distribution. The data in this database represent the monthly weight (in thousands of pounds) of each vegetable. In terms of monthly weight, describe each vegetable (onions and broccoli). If a month were randomly selected from the onion distribution, what is the probability that the weight would be more than 50,000? What is the probability that the weight would be between 25,000 and 35,000? If a month were randomly selected from the broccoli distribution, what is the probability that the weight would be more than 100,000? What is the probability that the weight would be between 135,000 and 170,000?

From the Hospital database, it can be determined that some hospitals admit around 50 patients per day. Suppose we select a hospital that admits 50 patients per day. Assuming that admittance only occurs within a 12-hour time period each day and that admittance is Poisson distributed, what is the value of lambda per hour for this hospital? What is the interarrival time for admittance based on this figure? Suppose a person was just admitted to the hospital. What the probability that it would be more than 30 minutes before the next person was admitted? What is the probability that there would be less than 10 minutes before the next person was admitted?

According to the International Data Corporation, HP is the leading company in the United States in PC sales with about 26% of the market share. Suppose a business researcher randomly selects 130 recent purchasers of PCs in the United States.

a. What is the probability that more than 39 PC purchasers bought an HP computer?

b. What is the probability that between 28 and 38 PC purchasers (inclusive) bought an HP computer?

c. What is the probability that fewer than 23 PC purchasers bought an HP computer?

d. What is the probability that exactly 33 PC purchasers bought an HP computer?

Let the Manufacturing database be the frame for a population of manufacturers to be studied. This database has 140 different SIC codes. Explain how you would take a systematic sample of size 10 from this frame. Examining the variables in the database, name two variables that could be used to stratify the population. Explain how these variables could be used in stratification and why each variable might produce important strata.

Use the Hospital database and determine the proportion of hospitals that are under the control of nongovernment not-for-profit organizations (category 2). Assume that this proportion represents the entire population of all hospitals. If you randomly selected 500 hospitals from across the United States, what is the probability that 45% or more are under the control of nongovernment not-for profit organizations? If you randomly selected 100 hospitals, what is the probability that less than 40% are under the control of nongovernment not-for profit organizations?

Using the Hospital database, construct a 90% confidence interval to estimate the average census for hospitals. Change the level of confidence to 99%. What happened to the interval? Did the point estimate change?

The Financial database contains financial data on 100 companies. Use this database as a sample and estimate the earnings per share for all corporations from these data. Select several levels of confidence and compare the results.

Using the frequency feature of the computer software, determine the sample proportion of the Hospital database under the variable “service” that are “general medical” (category 1). From this statistic, construct a 95% confidence interval to estimate the population proportion of hospitals that are “general medical.” What is the point estimate? How much error is there in the interval?

Do various financial indicators differ significantly according to type of company? Use a one-way ANOVA and the financial database to answer this question. Let Type of Company be the independent variable with seven levels (Apparel, Chemical, Electric Power, Grocery, Healthcare Products, Insurance, and Petroleum). Compute three one-way ANOVAs, one for each of the following dependent variables: Earnings Per Share, Dividends Per Share, and Average P/E Ratio. On each ANOVA, if there is a significant overall difference between Type of Company, compute multiple comparisons to determine which pairs of types of companies, if any, are significantly different.

In the Manufacturing database, the Value of Industrial Shipments has been recoded into four classifications (1–4) according to magnitude of value. Let this value be the independent variable with four levels of classifications. Compute a one-way ANOVA to determine whether there is any significant difference in classification of the Value of Industrial Shipments on the Number of Production Workers (dependent variable). Perform the same analysis using End-of-Year Inventories as the dependent variable. Now change the independent variable to Industry Group, of which there are 20, and perform first a one-way ANOVA using Number of Production Workers as the dependent variable and then a one-way ANOVA using End-of-Year Inventory as the dependent variable.

The hospital database contains data on hospitals from seven different geographic regions. Let this variable be the independent variable. Determine whether there is a significant difference in Admissions for these geographic regions using a one-way ANOVA. Perform the same analysis using Births as the dependent variable. Control is a variable with four levels of classification denoting the type of control the hospital is under (such as federal government or for-profit). Use this variable as the independent variable and test to determine whether there is a significant difference in the Admissions of a hospital by Control. Perform the same test using Births as the dependent variable.

The Consumer Food database contains data on Annual Food Spending, Annual Household Income, and Non-Mortgage Household Debt broken down by Region and Location. Using Region as an independent variable with four classification levels (four regions of the U.S.), perform three different one-way ANOVA’s—one for each of the three dependent variables (Annual Food Spending, Annual Household Income, Non-Mortgage Household Debt). Did you find any significant differences by region? If so, conduct multiple comparisons to determine which regions, if any, are significantly different.

Discuss the following Minitab output.

Develop a regression model from the Consumer Food database to predict Annual Food Spending by Annual Household Income. Discuss the model and its strength on the basis of statistics presented in this chapter. Now develop a regression model to predict Non-Mortgage Household Debt by Annual Household Income. Discuss this model and its strengths. Compare the two models. Does it make sense that Annual Food Spending and Non-Mortgage Household Debt could each be predicted by Annual Household Income? Why or why not?

Using the Hospital database, develop a regression model to predict the number of Personnel by the number of Births. Now develop a regression model to predict number of Personnel by number of Beds. Examine the regression output. Which model is stronger in predicting number of Personnel? Explain why, using techniques presented in this chapter. Use the second regression model to predict the number of Personnel in a hospital that has 110 beds. Construct a 95% confidence interval around this prediction for the average value of y.

Analyze all the variables except Type in the Financial database by using a correlation matrix. The seven variables in this database are capable of producing 21 pairs of correlations. Which are most highly correlated? Select the variable that is most highly correlated with P/E ratio and use it as a predictor to develop a regression model to predict P/E ratio. How did the model do?

Construct a correlation matrix for the six U.S. and international stock indicators. Describe what you find. That is, what indicators seem to be most strongly related to other indicators? Now focus on the three international stock indicators. Which pair of these stock indicators is most correlated? Develop a regression model to predict the DJIA by the Nikkei 225. How strong is the model? Develop a regression model to predict the DJIA by the Hang Seng. How strong is the model? Develop a regression model to predict the DJIA by the Mexico IPC. How strong is the model? Compare the three models.

Use the Manufacturing database to develop a multiple regression model to predict Cost of Materials by Number of Employees, New Capital Expenditures, Value Added by Manufacture, and End-of-Year Inventories. Discuss the results of the analysis.

Develop a regression model using the Financial database. Use Total Revenues, Total Assets, Return on Equity, Earnings Per Share, Average Yield, and Dividends Per Share to predict the average P/E ratio for a company. How strong is the model? Which variables seem to be the best predictors?

Using the international unemployment database, construct a stem-and-leaf plot for Italy. What does the plot show about unemployment for Italy over the past 40 years? What does the plot fail to show?

The Zumper National Rent Report lists the average monthly apartment rent in various locations in the United States. According to their report, the average cost of renting a one-bedroom apartment in Houston is $1,090. Suppose that the standard deviation of the cost of renting a one-bedroom apartment in Houston is $96 and that such apartment rents in Houston are normally distributed. If a one-bedroom apartment in Houston is randomly selected, what is the probability that the price is:

a. $1150 or more?

b. Between $1000 and $1200?

c. Between $950 and $1050?

d. Less than $800?

Suppose you are the CEO of a company such as Procter & Gamble in the financial database. What are some decisions that you might make in which you would consider decision alternatives? Name three arenas in which you would be making substantial strategic decisions (e.g., marketing, finance, production, and human resources). Delineate at least three decision alternatives in each of these arenas. Examine and discuss at least two states of nature that could occur under these decision alternatives in each arena.

Suppose you are the CEO of a hospital in the hospital database. You are considering expansion of the physical facility. What are some decision alternatives to consider? What are some states of nature that can occur in this decision-making environment? How would you go about calculating the payoffs for such a decision?

A carpet and rug manufacturer in the manufacturing database is faced with the decision of making expenditures in the form of machinery in anticipation of strong growth or not making the expenditures and losing market opportunity. Experts claim that there is about a 40% probability of having strong growth in the industry and a 60% probability of not having strong growth in the industry. If there is strong growth, the company will realize a payoff of $5,500,000 if the capital expenditure is made. Under strong growth, if the company does not make the capital expenditure, it will still realize a $750,000 payoff in new business, which it can handle with existing equipment. If there is not strong growth in the industry and the company has made the capital expenditure, the payoff will be −$2,000,000. If there is not strong growth and the capital expenditure has not been made, the company will receive a payoff of $500,000. Analyze this situation by using the decision analysis techniques presented in this chapter.

A dairy company in the Manufacturing database tests its quart milk container fills for volume in four-container samples. Shown here are the results of 10 such samples and the volume measurements in quarts. Use the information to construct both an x and an R chart for the data. Discuss the results. What are the centerline, LCL, and UCL for each of these charts?

Using the International Stock Market database, conduct a stepwise multiple regression procedure to predict the DJIA by the Nasdaq, the S&P 500, the Nikkei, the Hang Seng, the FTSE 100, and the IPC. Discuss the outcome of the analysis including the model, the strength of the model, and the predictors.

Develop a regression model using the Financial database. Use Total Revenues, Total Assets, Return on Equity, Earnings per Share, Average Yield, and Dividends per Share to predict the average P/E ratio for a company. How strong is the model? Use stepwise regression to help sort out the variables. Several of these variables may be measuring similar things. Construct a correlation matrix to explore the possibility of multicollinearity among the predictors.

Construct a correlation matrix for the Hospital database variables. Are some of the variables highly correlated? Which ones and why? Perform a stepwise multiple regression analysis to predict Personnel by Control, Service, Beds, Admissions, Census, Outpatients, and Births. The variables Control and Service will need to be coded as indicator variables. Control has four subcategories, and Service has two.

Use the Manufacturing database to develop a multiple regression model to predict Cost of Materials by Number of Employees, New Capital Expenditures, Value Added by Manufacture, Value of Industry Shipments, and End-of- Year Inventories. Create indicator variables for values of industry shipments that have been coded from 1 to 4. Use a stepwise regression procedure. Does multicollinearity appear to be a problem in this analysis? Discuss the results of the analysis.

Develop a multiple regression model to predict Annual Food Spending by Annual Household Income and Non-Mortgage Household Debt using the Consumer Food database. How strong is the model? Which of the two predictors seems to be stronger? Why?

Using the International Stock Market database, develop a multiple regression model to predict the Nikkei by the DJIA, the Nasdaq, the S&P 500, the Hang Seng, the FTSE 100, and the IPC. Discuss the outcome, including the model, the strength of the model, and the strength of the predictors.

Using the Manufacturing database as a sample, construct a 95% confidence interval for the population mean number of production workers. What is the point estimate? How much is the error of the estimate? Comment on the results.

Compute a Spearman’s rank correlation between New Capital Expenditures and End-of-Year Inventories in the Manufacture database. Is the amount spent annually on New Capital Expenditures related to the End-of-Year Inventories? Are these two variables highly correlated? Explain.

Use the following decision table to complete parts (a) through (c).

a. Draw a decision tree to represent this decision table.

b. Compute the expected monetary values for each decision and label the decision tree to indicate what the final decision would be.

c. Compute the expected payoff of perfect information. Compare this answer to the answer determined in part (b) and compute the value of perfect information.

Use a Kruskal-Wallis test to determine whether there is a significant difference between the four levels of Value of Industry Shipments on Number of Employees for the Manufacture database. Discuss the results.

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