AVALON Cosmetics sells door-to-door cosmetics much like Mary Kay. Women work as independent contractors for commissions and bonuses. Total company revenues have fallen 5% for each of the past two years! Customers report that they are highly satisfied with the product. Customers say the price is right and are repeat customers. In fact prices have been increased only to cover inflation over the past two years. Some concern has been expressed over the company's perception of the profile of its customers. Some managers feel the customers are primarily women staying at home with their children. However, recent articles about increasing numbers of working women made others question the profile. Based on some
existing data on customer history that is kept by the beauty consultants, three samples of 100 customers were selected from the summers of 1990, 1991, and 1992. The database complied contained the following information.
(Ratio variable)
Year Month Day Purchase Price Number of Contacts Time of Day Employed Age No. of Children
2003 6 12 3.53 1 1 0 35 2
2002 7 15 10.50 3 3 1 36 1
2004 8 20 15.55 2 2 1 26 0
The variables are defined as follows:
Year: Year in which purchase was made.
Month: Month purchase was made ,e.g., 6 = June, 7 = July, 8 = August
Day: Day of purchase
Purchase Price: Retail dollar amount of purchase
Number of Contacts: Number of times agent visited home before making contact with customer (Ratio)
Time of Day: 1 = Morning
2 = Afternoon
3 = Evening
Employed: 1 = Customer employed outside of home
0 = Otherwise
Age: Age in years
Number of Children: Number of children living at home
Answer the following questions about the database with the intention of examining the changing customer profile. Attempt to show how the changing profile helps explain the reduced total sales revenue. Provide recommendations on how the company might turn around the declining sales picture. The questions should lead you through the analysis and then you should make your final conclusions.
Use the file AVALON1.XLS
Question 19
The information below applies to problems 19 to 21.
At this point, the analyst determined that if it takes more contacts to reach a customer before a sale is made, the efficiency and profitability of the sales agent will be reduced. One of the managers at Avalon brought up the fact that one reason for lowered overall sales might be the lack of motivation and drive on the part of the sales agents.
In an effort to explore the profitability issue, the company wants to determine if over the past 3 years the average number of contacts required to write a purchase order has increased? What statistical technique would be used?
Answer
a. Regression
b. Analysis of Variance
c. Crosstabs
Question 20
What would be the F value and p value for the appropriate test?
Answer
a. T = 2.35 and p = .075
b. F = 63.63 and p = .000
Question 21
How many average contacts did it take in the three consecutive years of 2002, 2003, 2004?
Answer
a. 1.94, 2.92, 4.10
b. 2.48, 2.93, 3.62
Question 22
This material applies to problems 22 and 23.
Someone popped up with the question, " For the women working outside of the home (that is, not all cases), is there a significant difference in the average number of contacts based on the time of day that a sale is made? Basically, the manager wanted to know if there was a "best time of day to attempt to reach working women".
What is the statistical value and the p value for the appropriate test of hypothesis?
Answer
a. Chi Sq = 22.3 and p = .000
b. t = 5.6 and p = .000
c. F = 32.13 and p = .000
Question 23
Which time of the day has the fewest number of average contacts required to reach working women?
Answer
a. Morning
b. Afternoon
c. Evening
Question 24
This information applies to problems 24 to 30.
Another question was raised by management, "As the years pass, is that having an effect on the time of day that the sale is being made"? (REMEMBER TO SWITCH BACK TO ALL CASES)
Answer
a. Regression
b. Analysis of Variance
c. Crosstabs
Question 25
What would be the appropriate statistical values for the test?
Answer
a. F = 8.13 and p = .001
b. Chi Square - 44.82 and p = .000
c. Chi Square = 53.469 and p = .000
Question 26
What is the actual number of sales made in the mornings in 2002?
Answer
a. 35
b. 55
Question 27
What would be the expected number of sales in the mornings of 2002 if there was no relationship between year and the time of day?
Answer
a. 29.45
b. 39.67
Question 28
What is the actual number of sales made in the evenings in 2004?
Answer
a. 27
b. 57
Question 29
What would be the expected number of sales in the evenings of 2004 if there was no relationship between year and the time of the day?
Answer
a. 39.66
b. 31.33
Question 30
Based on the results of problems 26 - 29, the following "pattern" in repeatable data can be observed.
Answer
a. As the years are passing, there is no significant change in the number of sales in the differing portions of the day.
b. As the years are passing, there is a significant increase in the number of sales being made in the morning.
c. As the years are passing, there is a significant increase in the number of sales being made in the evening.
Question 31
This information applies to problems 31 to 33.
The question of the changing employment status of the present customers as the years are passing seemed to be a recurrent theme in the discussion of the data.
The company wants to know if the employment status is significantly related to the year of the sale? What statistical values are appropriate?
Answer
a. Chi-Square = 23.22 and p = 0
b. Chi square = 30.437 and p = 0
Question 32
What percentage of women were employed in 2002,2003 and 2004?
Answer
a. 26%, 39%, 64%
b. 36%, 64%, 100%
Question 33
What basic repeatable pattern seems to be present in the appropriate analysis.
Answer
a. As the years pass, more women are staying at home.
b. As the years pass, more women are leaving the home to work.
c. As the years pass, no significant pattern as to working or not working has emerged.
Question 34
One of the managers had by this time developed some interest in determining if there was a generalized equation that would possibly predict the "average purchase price" of a customer. If the important factors could be isolated, that might lead to a better defining of the "target market" of customers. After much discussion, the managers decided that they would like to determine if the purchase price by a customer might be related to their age (do younger women buy more make-up?), or the number of children they have (do women with fewer children buy more make-up), and the time of day that the customer is contacted (something that a sales program might emphasize) and finally whether the customer is employed or not (since once that fact is known, the marketing program might be redirected to a given market segment).
NOTE: Only consider the independent variables mentioned, that is, age, number of children, time of day, and employment status. Also, be sure to only include statistically significant factors in the equation. Be sure to make indicator variables when necessary.
Using stepwise regression to find the best equation possible (use F default values) , what is the best multivariate model for the problem.
Answer
a. Purchase Price = 25.64 + .032 Age - .45 No. of Children - 1.63 Time of Day
b. Purchase Price = 27.16 -.84 No. of Children - 1.95 Time of Day1
Question 35
Once you have used stepwise regression to find the best model, you should do a regular regression with just the indicated variables in the model. Do that now.
Based on the correct model, what percent of the variation in purchase price can be related to the significant factors identified?
Answer
a. 5.84%
b. 25.5%
Question 36
On the average, how much less is the average purchase price if the purchase is made in the morning?
Answer
a. - $1.95
b. $1.556
Question 37
On the average, how much change in the average purchase price will occur for each additional child in the family?
Answer
a. .0046
b. - $0.84
Question 38
Is the age of the customer a significant factor in predicting purchase price?
Answer
a. Yes
b. No
Question 39
Is the employment status important in determining the purchase price of an individual?
Answer
a. Yes
b. No
Question 40
If a woman is 32 years of age, has 3 children, is contacted in the morning and is employed outside of the home, on the average, what will be the purchase price of the order?
Answer
a. $22.68
b. $21.45
Question 41
For this same woman, what would be the prediction range of purchase order values that could be expected?
Answer
a. 20.44 to 22.26
b. 10.16 to 35.21