Real difference between the chains of grocery stores

Question

Assignment:

Q1: Deb is the owner and manager of Deb's Specialty Coffees and Desserts, a small Oregon firm that roasts coffee beans and retails bulk beans to grocery stores, as well as desserts targeted to health conscious consumers. Deb is curious as to whether her new publicity campaign will help boost sales in the stores that carry her products. During a recent month, she hired unemployed State workers to provide free samples to grocery shoppers in one of the chains of Oregon grocery stores that she supplies. She hopes that the cost of the campaign will be more than offset by increased unit sales. The total cost to Deb is $1,500 each month for the cost of supplies, renting space in the stores, and salaries for handing out the free samples.

Since she hasn't used in-store testers before, Deb is uncertain about whether her efforts will actually result in increased sales. If sales increase to at least cover the cost of the campaign, she'll be more likely to repeat the ads at a later date. She would like to know whether unit sales increased significantly as a result of the testers. If sales do increase, Deb would like answers to the following questions:

1. How large an increase was realized? How confident can she be in the results?
2. Was there a real difference between the two chains of grocery stores?
3. How much confidence can be placed in the results of the analysis?

In order to determine the impact of the ads, Deb recorded daily unit sales of coffee beans for one month (August 2005) in two of the grocery store chains that she supplies, in order to establish a basis of comparison. Sales have been remarkably consistent on a month-to-month basis between the two chains over the past two years, so she feels that this is an effective baseline. She then hired testers to hand out free samples and recorded daily sales for one of the chains. The other chain sold coffee as had been done in the past. The data for the two chains is listed above. Deb has heard about your excellent work during the last five weeks of RES 341 and has hired you to analyze and present the raw data to her in a way that makes sense to someone who has never taken a statistics class.

The numbers shown represent pounds sold of coffee per day. She makes a gross profit of $5.50 for each pound sold. Her net profit has been $3.00 for each pound.

For RES 342, Week Five:
Specifically, you are asked to provide the following information to Deb in the form of a professional business memo that summarizes the data and makes at least two business recommendations:

Calculate and explain descriptive statistics and variation for these data sets, .

Discuss similarities and differences. What is the most efficient way to compare the two data sets?

The next three worksheets contain additional questions that should be included in your business memo to enrich your discussion and analysis.

Your memo will be graded based on the depth of your analysis and how completely you answer each question. Each team member is expected to participate in the data analysis and constructing the final memorandum. The calculations should be included as appendices to your memo.

Unit Sales by Day for Deb's Specialty Coffees
August 2005  - Store Chain #1 (control group)
Sunday	Monday	Tuesday	Wednesday	Thursday	Friday	Saturday
	141	126	169	130	121	217
162	134	113	124	163	146	174
170	146	158	179	132	111	156
187	133	142	153	130	148	182
181	148	176	195
August 2005 - Store Chain #2 (experimental group)
Sunday	Monday	Tuesday	Wednesday	Thursday	Friday	Saturday
	153	126	114	180	187	275
274	184	176	146	191	162	249
213	135	187	168	157	174	225
234	176	165	154	226	184	198
234	198	172	186

Q2: Deb wants to find out if the product location in the store has any effect on the sale of her specialty coffee beans. Three different store locations are to be considered; front, middle, and rear. A random sample of 27 stores is selected with 9 stores randomly assigned to each aisle location. At the end of a one-week trial, .sales volume for each location (in hundreds of dollars) is charted above.

Compare the three locations using ANOVA, and test the hypothesis that there is a difference between groups, then make a recommendation to Deb.

Specialty Coffee Sales
Front	Middle	Rear
8.82	8.21	8.57
9.26	6.65	8.5
8.7	7.44	9.11
8.97	7.95	8.2
8.64	8.2	8.32
8.29	7.75	7.88
9.45	8.84	9.9
9.42	8.4	9.43
9.25	7.98	8.85

Q3: Deb's coffee company sells beans, roasters, and brewing machines. Recently, Deb held a contest for her sales staff to see how many roasting and brewing machines they could sell in a month. Each sales rep logged the number of cold calls they made and the number of coffee roasters they sold. The results are in the table at left.

Use Excel to run a regression on this data and then answer the following questions.
1. What is the coefficient of correlation? Is it significant? How do you know?

2. How much of the variation in the dependent variable is left unexplained?

3. What is the linear regression equation?

4. Are cold calls a good predictor of number of machines sold at an alpha of .05? How do you know? How about an alpha of .01

5. Predict the number of machines sold for a sales rep who makes 75 cold calls during a given month.

6. Are there other variables that you think might be good predictors? What are they and why do you think they would enhance this predictive model?

Sales Rep	Cold calls	Machines sold
Tom	30	20
Jeff	60	40
Brian	40	20
Greg	60	30
Susan	30	10
Carlos	40	10
Rich	40	20
Mike	50	20
Mark	30	20
Sonia	70	30

Q4: You've been asked to provide expertise in quantitative analysis on Deb's newest business venture. She's experimenting with creating a new form of frozen dessert to appeal to trendy health conscious consumers. Specifically, she's trying to replace the "cream" in ice cream with a more nutritious substitute. Sadly, consumers have yet to appreciate her efforts and sales have been dismal. Instead of giving up, she's hired a new crew of lactose-intolerant chefs who have developed four new frozen non-dairy desserts. Knowing that you have mastered various ways to quantify data, she asks you to test whether consumers have a preference for any of the new items.

You prepare a blind taste test that asks the test subjects to select their favorite flavor, and arrange with a local health food store to use their customer database, offering each customer $20 to participate in your study. You select 100 random customers and ask them to taste each flavor, in no particular order. You then record the number of times each dessert flavor was selected as the favorite. The results of your study are as follows:

Dessert	Observed	Expected
Sweet Potato Pops	38
Sugar Beet Treats	13
Tofu Surprise	47
Frozen Bransicles	2

a. What are the hypotheses for your research design?

b. Compute the expected frequencies, assuming that customers have no preference for any of the flavors.

c. What is the table value for the c2 statistic at a .05 level of significance? State your decision rule.

d. Compute the c2 for this goodness-of-fit test and reach a decision.

e. On the basis of your results, should Deb rush to market with any of the new flavors? Explain the rationale for your recommendation and include a critique of the sampling methodology and research design. If you had been in charge of this project from the beginning, what would you have done differently?

Her next question is whether there is a relationship between gender and flavor preference. You take a random sample of 150 shoppers and categorize them in the following contingency table (none of them expressed any interest in the frozen bransicles):

		Flavor
		Sweet Potato Pops	Sugar Beet Treats	Tofu Surprise
Gender	Male	39	38	8
	Female	20	40	5

f. What are the hypotheses for your research design?

g. Compute the expected frequencies.

h. What is the table value for the c2 statistic at a .01 level of significance? State your decision rule.

i.  Compute the c2 for this contingency table test and reach a decision. Is there a gender effect on flavor preference?

j. On the basis of your results, should Deb market her products differently to men and women? Explain the rationale for your recommendation and include a critique of the sampling methodology and research design. If you had been in charge of this project from the beginning, what would you have done differently?