Instructions The major shopping areas in the community of Sp

Instructions

The major shopping areas in the community of Springdale include Springdale Mall, West Mall, and the downtown area on Main Street. A telephone survey has been conducted to identify strengths and weaknesses of these areas and to find out how they fit into the shopping activities of local residents.

NOTE: Be sure to use five (5) decimal places for your probabilities in the report, as some of them will be quite small.

1. Set up a contingency table for the appropriate variables given below, and then determine the following probabilities:

a. [variables 4 and 26] Given that the random respondent is a female, what is the probability that she spends at least $15 during a trip to Springdale Mall? Is a male more likely or less likely than a female to spend at least $15 during a visit to this area?

b. [variables 5 and 26] Given that the random respondent is a female, what is the probability that she spends at least $15 during a trip to Downtown? Is a male more likely or less likely than a female to spend at least $15 during a visit to this area?

c. [variables 6 and 26] Given that the random respondent is a female, what is the probability that she spends at least $15 during a trip to West Mall? Is a male more likely or less likely than a female to spend at least $15 during a visit to this area?

d. Based on the preceding probabilities, rank the shopping areas where males and females are most likely to least likely to spend $15 or more during a shopping visit.

The variables in the survey were as follows:

How Much the Respondent Spends during a Trip to Each Area (Variables 4–6)

4. Springdale Mall

5. Downtown

6. West Mall

$200 or more

(1)

(1)

(1)

$150–under $200

(2)

(2)

(2)

$100–under $150

(3)

(3)

(3)

$ 50–under $100

(4)

(4)

(4)

$ 25–under $50

(5)

(5)

(5)

$ 15–under $25

(6)

(6)

(6)

less than $15

(7)

(7)

(7)

Which Shopping Area Best Fits Each Description (Variable 11)

Springdale

Mall

Downtown

West

Mall

No

Opinion

11. High quality of goods

(1)

(2)

(3)

(4)

Information about the Respondent (Variable 26) Gender: (1) = Male       (2) = Female

The data obtained in the survey is as follows:

	4. Springdale Mall	5. Downtown	6. West Mall
$200 or more	(1)	(1)	(1)
$150–under $200	(2)	(2)	(2)
$100–under $150	(3)	(3)	(3)
$ 50–under $100	(4)	(4)	(4)
$ 25–under $50	(5)	(5)	(5)
$ 15–under $25	(6)	(6)	(6)
less than $15	(7)	(7)	(7)

Solution

(a)No. of females=88

No.of females spending atleast $15 at Springdale mall=88-19=69

Probability that a female spends atleast $15 at Springdale mall=69/88=0.784

No. of males=62

No.of males spending atleast $15 at Springdale mall=62-23=39

Probability that a male spends atleast $15 at Springdale mall=39/62=0.629

Thus at Springdale mall a female is more likely to spend atleast $15 than a male.

(b)

No. of females=88

No.of females spending atleast $15 at Downtown mall=88-45=43

Probability that a female spends atleast $15 at Downtown mall=43/88=0.489

No. of males=62

No.of males spending atleast $15 at Downtown mall=62-25=37

Probability that a male spends atleast $15 at Downtown mall=37/62=0.597

Thus at Downtown mall a male is more likely to spend atleast $15 than a female.

(c)

No. of females=88

No.of females spending atleast $15 at West mall=88-38=50

Probability that a female spends atleast $15 at West mall=50/88=0.568

No. of males=62

No.of males spending atleast $15 at West mall=62-34=28

Probability that a male spends atleast $15 at West mall=28/62=0.452

Thus at West mall a female is more likely to spend atleast $15 than a male.

(d)For males,Probability of spending more than $15 at different malls can be ordered as-

Springdale Mall>Downtown>West Mall

For females,Probability of spending more than $15 at different malls can be ordered as-

Springdale Mall>West Mall>Downtown