mathematics

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

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