Math Problems

Math Problems
Mercedes Goes After Younger Buyers
Mercedes and BMW have been competing head-to-head for market share in the luxury-car market for more than four decades. Back in 1959, BMW (BayerischeMotorenWerke) almost went bankrupt and nearly sold out to Daimler-Benz, the maker of Mercedes-Benz cars. BMW was able to recover to the point that in 1992 it passed Mercedes in worldwide sales. Among the reasons for BMW’s success was its ability to sell models that were more luxurious than previous models but still focused on consumer quality and environmental responsibility. In particular, BMW targeted its sales pitch to the younger market, whereas Mercedes retained a more mature customer base.
In response to BMW’s success, Mercedes has been trying to change their image by launching several products in an effort to attract younger buyers who are interested in sporty, performance-oriented cars. BMW, influenced by Mercedes, is pushing for more refinement and comfort. In fact, one automotive expert says that Mercedes wants to become BMW, and vice versa. However, according to one recent automotive expert, the focus is still on luxury and comfort for Mercedes while BMW focuses on performance and driving dynamics. Even though each company produces many different models, two relatively comparable coupe automobiles are the BMW 3 Series Coupe 335i and the Mercedes C350 Coupe. In a recent year, the national U.S. market price for the BMW 3 Series Coupe 335i was $41,022 and for the Mercedes C350 Coupe $45,493. Gas mileage for both of these cars is around 17 mpg in town and 25 mpg on the highway.

1. Suppose Mercedes is concerned that dealer prices of the C350 Coupe are not consistent and that even though the average price is $45,493, actual prices are normally distributed with a standard deviation of $2,981. Suppose also that Mercedes believes that at $44,000, the C350 is priced out of the BMW 3 Series Coupe 335i market. What percentage of the dealer prices for the Mercedes C350 Coupe is more than $44,000 and hence priced out of the BMW 3 Series Coupe 335i market? The average price for a BMW 3 Series Coupe 335i is $41,022. Suppose these prices are also normally distributed with a standard deviation of $2,367. What percentage of BMW dealers is pricing the BMW 3 Series Coupe 335i at more than the average price of a Mercedes C350 Coupe? What might this mean to BMW if dealers were pricing the 3 Series Coupe 335i at this level? What percentage of Mercedes dealers is pricing the C350 Coupe at less than the average price of a BMW 3 Series Coupe 335i?

2. Suppose that highway gas mileage rates for both of these cares are uniformly distributed over a range of from 20 to 30 mpg. What proportion of these cars would fall into the 22 to 27 mpg range? Compute the proportion of cars that get more than 28 mpg. What proportion of cars would get less than 23 mpg?

3.Suppose that in one dealership an average of 1.37 CLKs is sold every 3 hours (during a 12-hour showroom day) and that sales are Poisson distributed. The following Excel-produced probabilities indicate the occurrence of different intersales times based on this information. Study the output and interpret it for the salespeople. For example, what is the probability that less than an hour will elapse between sales? What is the probability that more than a day (12-hour day) will pass before the next sale after a car has been sold? What can the dealership managers do with such information? How can it help in staffing? How can such information be used as a tracking device for the impact of advertising? Is there a chance that these probabilities would change during the year? If so, why?

Portion of 3-Hour Time Frame Cumulative Exponential Probabilities from Left
0.167 0.2045
0.333 0.3663
0.667 0.5990
1 0.7459
2 0.9354
3 0.9836
4 0.9958
5 0.9989

Shell Attempts to Return to Premiere Status
The Shell Oil Company, which began about 1912, had been for decades a household name as a quality oil company in the United States. However, by the late 1970s much of its prestige as a premiere company had disappeared. How could Shell regain its high status?
In the 1990s, Shell undertook an extensive research effort to find out what it needed to do to improve its image. As a first step, Shell hired Responsive Research and the Opinion Research Corporation to conduct a series of focus groups and personal interviews among various segments of the population. Included in these were youths, minorities, residents in neighborhoods near Shell plants, legislators, academics, and present and past employees of Shell. The researchers learned that people believe that top companies are integral parts of the communities in which the companies are located rather than separate entities. These studies and others led to the development of materials that Shell used to explain their core values to the general public.
Next, PERT Survey Research ran a large quantitative study to determine which values were best received by the target audience. Social issues emerged as the theme with the most support. During the next few months, the advertising agency of Ogilvy & Mather, hired by Shell, developed several campaigns with social themes. Two market research companies were hired to evaluate the receptiveness of the various campaigns. The result was the “Count on Shell” campaign, which featured safety messages with useful information about what to do in various dangerous situations.
A public “Count on Shell” campaign was launched in February 1998 and met with considerable success: the ability to recall Shell advertising jumped from 20% to 32% among opinion influencers, and more than 1 million copies of Shell’s free safety brochures were distributed. By promoting itself as a reliable company that cares, Shell seems to be regaining its premiere status.
Today, Shell initiates and supports several programs in which the company and employees are involved in community and civic activities. These programs range from local improvement projects to fundraising events for regional nonprofit organizations. According to company sources, “every year, more than 1,500 Shell employees, retirees and their family members contribute, on average, more than 40,000 hours for company-sponsored volunteer initiatives nationwide” in the United States. Some of these include America’s WETLAND Campaign, Shell’s Workforce Development Initiative, and United Way campaigns. Shell U.S. has been a strong supporter of the Points of Light Foundation; and each fall, Shell volunteers participate in the cleaning of beaches in Texas, Louisiana, and California. In addition, Shell sponsors the Shell Houston Open PGA golf tournament, which has raised $50 million since 1974 for various children’s charity organizations.

1.Suppose you were asked to develop a sampling plan to determine what a “premiere company” is to the general public. What sampling plan would you use? What is the target population? What would you use for a frame? Which of the four types of random sampling discussed in this chapter would you use? Could you use a combination of two or more of the types (two-stage sampling)? If so, how?
2. It appears that at least one of the research companies hired by Shell used some stratification in their sampling. What are some of the variables on which they are stratified? If you were truly interested in ascertaining opinions from a variety of segments of the population with regard to opinions on “premiere” companies or about Shell, what strata might make sense? Name at least five and justify why you would include them.
3. Suppose that in 1979 only 12% of the general adult U.S. public believed that Shell was a “premiere” company. Suppose further that you randomly selected 350 people from the general adult U.S. public this year and 25% said that Shell was a “premiere” company. If only 12% of the general adult U.S. public still believes that Shell is a “premiere” company, how likely is it that the 25% figure is a chance result in sampling 350 people? Hint: Use the techniques in this chapter to determine the probability of the 25% figure occurring by chance.
4. PERT Survey Research conducted quantitative surveys in an effort to measure the effectiveness of various campaigns. Suppose on their survey instrument, they used a continuous scale of from 0 to 10 where 0 denotes that the campaign is not effective at all, 10 denotes that the campaign is extremely effective, and other values fall in between to measure the effectiveness. Suppose also that a particular campaign received an average of 3.6 on the scale with a standard deviation of 1.4 early in the tests. Later, after the campaign had been critiqued and improved, a survey of 35 people was taken and a sample mean of 4.0 was recorded. What is the probability of this sample mean or one greater occurring if the actual population mean is still just 3.6? Based on this probability, do you think that a sample mean of 4.0 is just a chance fluctuation on the 3.6 population mean, or do you think that perhaps it indicates the population mean is now greater than 3.6? Support your conclusion. Suppose a sample mean of 5.0 is attained. What is the likelihood of this result occurring by chance when the population mean is 3.6? Suppose this higher mean value actually occurs after the campaign has been improved. What does it indicate?
The Container Store
In the late 1970s, Kip Tindell (chairman and CEO), Garrett Boone (Chairman Emeritus), and John Mullen (architect) drew up plans for a first of a kind retail store specializing in storage solutions for both the home and the office. The vision that they created was realized when on July 1, 1978, the Container Store opened its doors in a small 1600-square-foot retail space in Dallas. The store was stocked with products that were devoted to simplifying people’s lives, such as commercial parts bins, wire drawers, mailboxes, milk crates, wire leaf burners, and many others. Some critics even questioned whether a store selling “empty boxes” could survive. However, the concept took off, and in the past 33 years, the company has expanded coast to coast in the United States with stores in 49 locations. Now headquartered in Coppell, Texas, the Container Store has 4000 employees and annual revenues of over $650 million.
Besides their innovative product mix, some of the keys to the success of the Container Store are the enthusiasm with which their employees work, the care that employees give to the customer, and employee knowledge of their products. For 12 straight years, the Container Store has made Fortune magazine’s list of “100 Best Companies to Work For.” Generally rated in the top 40 of this list each year, the company was number 1 for the first two years that they applied for consideration. Their current president, Melissa Reiff, credits the company’s devotion to recruiting and retaining a highly qualified workforce as one of the keys to its success. Company sources say that the Container Store offers more than 240 hours of formal training for full-time employees the first year of employment with the company and that this compares to about 8 hours of such training with other companies in the industry. According to company sources, the Container Store believes that their employees are their number one stakeholder and “The Container Store is an absolutely exhilarating and inspiring place to shop and an equally exciting place to work.”
In addition to innovative products and motivated employees, the Container Store has embraced a commitment to the environment. Chairman Emeritus Garrett Boone says that they firmly believe that there is no conflict between economic prosperity and environmental stewardship. The Container Company is embracing sustainability as a key to their economic future. As part of this effort, they sell eco-friendly products, use highly efficient HVAC units in their stores and warehouses, sponsor an employee purchase program for compact fluorescent lights, are switching from neon to LED lighting in all exterior signage, and offer an employee battery and light bulb recycling program.
1. Among other things, the Container Store has grown and flourished because of strong customer relationships, which include listening to customer needs, containing products that meet customer needs, having sales people who understand both customer needs and the products, and creating a store environment that is customer friendly both in layout and in culture. Suppose company management wants to formally measure customer satisfaction at least once a year and develops a brief survey that includes the following four questions. Suppose that the survey was administered to 115 customers with the following results. Use techniques presented in this chapter to analyze the data to estimate the population responses to these questions.
Question Yes No
1. Compared to most other stores that you shop in, is the Container Storemore customer friendly? 73 42
2. Most of the time, this store has the number and type of home or office storage solution that I need. 81 34
3. The salespeople at this store appear the be particularly knowledgeable of their products. 88 27
4. Store hours are particularly convenient for me. 66 49

2. The Container Store is well known as a great company to work for. In addition, company management states that their employee is their number one stakeholder. Suppose in spite of their history as an employee-friendly company, management wants to measure employee satisfaction this year to determine if they are maintaining this culture. A researcher is hired by the company who randomly selects 21 employees and asks them to complete a satisfaction survey under the supervision of an independent testing organization. As part of this survey, employees are asked to respond to questions by providing a score of from 0 to 50 along a continuous scale, where 0 denotes no satisfaction and 50 denotes the utmost satisfaction. Assume that the data are normally distributed in the population. The questions and the results of the survey are shown below. Analyze the results by using techniques from this chapter. Discuss your findings.
Question Mean Standard Deviation
1. Are you treated fairly by the company as an employee? 42.4 5.2
2. Has the company given you the training that you need to do the job adequately? 44.9 3.1
3. Does management seriously consider your input in making decisions about the store? 38.7 7.5
4. Is your physical work environment acceptable? 35.6 9.2
5. Is the compensation for your work adequate and fair? 34.5 12.4
6. Overall, do you feel that company management really cares about you as a person? 41.8 6.3
DiGiorno Pizza: Introducing a Frozen Pizza to Compete with Carry-out
Kraft Foods successfully introduced DiGiorno Pizza into the marketplace in 1996, with first year sales of $120 million, followed by $200 million in sales in 1997. It was neither luck nor coincidence that DiGiorno Pizza was an instant success. Kraft conducted extensive research about the product and the marketplace before introducing this product to the public. Many questions had to be answered before Kraft began production. For example, why do people eat pizza? When do they eat pizza? Do consumers believe that carry-out pizza is always more tasty?
SMI-Alcott conducted a research study for Kraft in which they sent out 1000 surveys to pizza lovers. The results indicated that people ate pizza during fun social occasions or at home when no one wanted to cook. People used frozen pizza mostly for convenience but selected carry-out pizza for a variety of other reasons, including quality and the avoidance of cooking. The Loran Marketing Group conducted focus groups for Kraft with women aged 25 to 54. Their findings showed that consumers used frozen pizza for convenience but wanted carry-out pizza taste. Kraft researchers realized that if they were to launch a successful frozen pizza that could compete with carry-out pizza, they had to develop a frozen pizza that (a) had restaurant takeout quality, (b) possessed flavor variety, (c) was fast and easy to prepare, and (d) had the convenience of freezer storage. To satisfy these seemingly divergent goals, Kraft developed DiGiorno Pizza, which rises in the oven as it cooks. This impressed focus group members, and in a series of blind taste tests conducted by Product Dynamics, DiGiorno Pizza beat out all frozen pizzas and finished second overall behind one carry-out brand.
DiGiorno Pizza has continued to grow in sales and market share over the years. By 2005, sales had topped the $600 million mark, and DiGiorno Pizza held nearly a quarter of the market share of frozen pizza sales. In each of the last two quarters of 2009, DiGiorno sales increased 20%. On January 6, 2010, Kraft agreed to sell its North American frozen pizza business, including its DiGiorno products, to Nestlé for $3.7 billion.

Think about the market research that was conducted by Kraft and the fact that they used several companies.
1. What are some of the populations that Kraft might have been interested in measuring for these studies? Did Kraft actually attempt to contact entire populations? What samples were taken? In light of these two questions, how was the inferential process used by Kraft in their market research? Can you think of any descriptive statistics that might have been used by Kraft in their decision-making process?
2. In the various market research efforts made by Kraft for DiGiorno, some of the possible measurements appear in the following list. Categorize these by level of data. Think of some other measurements that Kraft researchers might have made to help them in this research effort, and categorize them by level of data.
a. Number of pizzas consumed per week per household
b. Age of pizza purchaser
c. Zip code of the survey respondent
d. Dollars spent per month on pizza per person
e. Time in between purchases of pizza
f. Rating of taste of a given pizza brand on a scale from 1 to 10, where 1 is very poor tasting and 10 is excellent taste
g. Ranking of the taste of four pizza brands on a taste test
h. Number representing the geographic location of the survey respondent
i. Quality rating of a pizza brand as excellent, good, average, below average, poor
j. Number representing the pizza brand being evaluated
k.Sex of survey respondent

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