QUESTION 1

1. The following material covers the final case.

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.MTW from blackboard.

What percent of the sample was taken in 2002?

a.

33.3%

b.

50%

2.44 points

QUESTION 2

1. What percent of the sample was taken in August?

a.

28.72%

b.

12.67%

2.44 points

QUESTION 3

1. What percent of the sales orders were written during the afternoon?

a.

29%

b.

68.7%

2.44 points

QUESTION 4

1. What percent of the sales orders were written during the afternoon in 2004 ?

a.

20%

b.

68.7%

2.44 points

QUESTION 5

1. What is the average dollar purchase order over the entire 3 year period?

a.

$24.60

b.

$23.02

2.44 points

QUESTION 6

1. What is the average number of contacts that a sales agent must make to get a sale (over the entire 3 year period)?

a.

2.15

b.

2.98

2.44 points

QUESTION 7

1. The goal of the sales person would be to make only 1 contact to get a purchase order. What percentage of times does the sales agent actually make a sale with only one contact?

a.

21.67%

b.

23%

2.44 points

QUESTION 8

1. This material applies to questions 8 – 11.

The analyst wanted to know if the average purchase price of each order was significantly different based on the year of the sample.

What is the null hypothesis for the problem?

a.

Ho: The average purchase price is different for the different years

b.

Ho: The average purchase price is the same for the different years

2.44 points

QUESTION 9

1. What is the F value and p-value for the test?

a.

F = 50.14 and p = .000

b.

F = 12.60 and p = .061

2.44 points

QUESTION 10

1. What is the average purchase price for the three years in question?

a.

21.7, 21.7, 21.7

b.

21.06, 23.82, 28.93

2.44 points

QUESTION 11

1. What Tukey range values establishes if the average purchase price in 2002 is significantly different from the average purchase price in 2003?

a.

.892 to 4.628

b.

6.007 to 9.743

2.44 points

QUESTION 12

1. This information applies to problems 12 and 13.

Some at Avalon Cosmetics were concerned that the time of day when the sale was made would significantly affect the purchase price.

What is the p value for the approriate test of hypothesis?

a.

.102

b.

.016

2.44 points

QUESTION 13

1. What would be the approriate conclusion to the hypothesis test?

a.

Accept Ho: I am not at least 95% sure that the average sales price is different for the different times of day.

b.

Accept Ha: I am at least 95% sure that the average sales price is different for the different times of day.

c.

Accept Ha: I am at least 95% sure that the average sales price is the same for the different times of day.

2.44 points

QUESTION 14

1. This material applies to questions 14 to 18.

Every time that a customer service saleswoman has to return to try to catch a customer, extra time and effort are involved. However, if the customer feels guilty about causing the representative to return more than one time, then maybe they may buy significantly more cosmetics … plus they may be out of more goods due to the unexpected time since the last successful contact (that is, an actual placed sales order). Does the expected purchase price for an order increase as the number of contacts increases?

What type of analysis should be performed?

a.

Regression

b.

Analysis of Variance

c.

Crosstabs

2.44 points

QUESTION 15

1. What is the t value and p value for the test?

a.

T = 5.43 and p = .000

b.

T = 3.23 and p = .001

2.44 points

QUESTION 16

1. On the average, how much more does a customer buy for each additional time the customer service representative goes to the house?

a.

$2.10 per visit

b.

$0.74 per visit

2.44 points

QUESTION 17

1. If a customer service agent makes only 30% on gross margin, what would be the expected increase in revenue for each additional contact attempt? Note: This answer is not found from the computer but is a business question that you need to answer.

a.

$.22 per additional contact

b.

$.63 per additional contact

2.44 points

QUESTION 18

1. What percent of the variation in purchase price can be associated with the variation in the number of contacts?

a.

3.4%

b.

62.3%

2.44 points

QUESTION 19

1. 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?

a.

Regression

b.

Analysis of Variance

c.

Crosstabs

2.44 points

QUESTION 20

1. What would be the F value and p value for the appropriate test?

a.

T = 2.35 and p = .075

b.

F = 63.63 and p = .000

2.44 points

QUESTION 21

1. How many average contacts did it take in the three consecutive years of 2002, 2003, 2004?

a.

1.94, 2.92, 4.10

b.

2.48, 2.93, 3.62

2.44 points

QUESTION 22

1. 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?

a.

Chi Sq = 22.3 and p = .000

b.

t = 5.6 and p = .000

c.

F = 32.13 and p = .000

2.44 points

QUESTION 23

1. Which time of the day has the fewest number of average contacts required to reach working women?

a.

Morning

b.

Afternoon

c.

Evening

2.44 points

QUESTION 24

1. 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)

a.

Regression

b.

Analysis of Variance

c.

Crosstabs

2.44 points

QUESTION 25

1. What would be the appropriate statistical values for the test?

a.

F = 8.13 and p = .001

b.

Chi Square – 44.82 and p = .000

c.

Chi Square = 53.469 and p = .000

2.44 points

QUESTION 26

1. What is the actual number of sales made in the mornings in 2002?

a.

35

b.

55

2.44 points

QUESTION 27

1. 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?

a.

29.45

b.

39.67

2.44 points

QUESTION 28

1. What is the actual number of sales made in the evenings in 2004?

a.

27

b.

57

2.44 points

QUESTION 29

1. 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?

a.

39.66

b.

31.33

2.44 points

QUESTION 30

1. Based on the results of problems 26 – 29, the following “pattern” in repeatable data can be observed.

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.

2.44 points

QUESTION 31

1. 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?

a.

Chi-Square = 23.22 and p = 0

b.

Chi square = 30.437 and p = 0

2.44 points

QUESTION 32

1. What percentage of women were employed in 2002,2003 and 2004?

a.

26%, 39%, 64%

b.

36%, 64%, 100%

2.44 points

QUESTION 33

1. What basic repeatable pattern seems to be present in the appropriate analysis.

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.

2.44 points

QUESTION 34

1. 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.

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

2.44 points

QUESTION 35

1. 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?

a.

5.84%

b.

25.5%

2.44 points

QUESTION 36

1. On the average, how much less is the average purchase price if the purchase is made in the morning?

a.

– $1.95

b.

$1.556

2.44 points

QUESTION 37

1. On the average, how much change in the average purchase price will occur for each additional child in the family?

a.

.0046

b.

– $0.84

2.44 points

QUESTION 38

1. Is the age of the customer a significant factor in predicting purchase price?

a.

Yes

b.

No

2.44 points

QUESTION 39

1. Is the employment status important in determining the purchase price of an individual?

a.

Yes

b.

No

2.44 points

QUESTION 40

1. 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?

a.

$22.68

b.

$21.45

2.44 points

QUESTION 41

1. For this same woman, what would be the prediction range of purchase order values that could be expected?

a.

20.44 to 22.26

b.

10.16 to 35.21

2.44 points

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