Homework SourseSpringdale Shopping Survey Instructions The major shopping a
Springdale Shopping Survey
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.
The contingency tables and relative frequency probabilities in this exercise are based on the Springdale Shopping Survey database. Information like that gained from the two parts of this exercise could provide helpful insights into the nature of the respondents, their perceptions, and their spending behaviors. In particular, part 2 focuses on how conditional probabilities related to spending behavior might vary, depending on the gender of the respondent.
NOTE: Be sure to use five (5) decimal places for your probabilities in the report, as some of them will be quite small.
Based on the relative frequencies for responses to each variable, determine the probability that a randomly selected respondent from:
[variable 4] spends at least $15 during a trip to Springdale Mall.
[variable 5] spends at least $15 during a trip to Downtown.
[variable 6] spends at least $15 during a trip to West Mall.
Comparing the preceding probabilities, rank the areas from strongest to weakest in terms of the amount of money a shopper spends during a typical shopping visit.
Based on the relative frequencies for responses to each variable, determine the probability that a randomly selected respondent from
[variable 11] feels that Springdale Mall has the highest-quality goods.
[variable 11] feels that Downtown has the highest-quality goods.
[variable 11] feels that West Mall has the highest-quality goods.
Comparing the preceding probabilities, rank the areas from strongest to weakest in terms of the quality of goods offered.
Set up a contingency table for the appropriate variables given, and then determine the following probabilities:
[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?
[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?
[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?
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) P(spends at least $15 during a trip to Springdale Mall) = No. of persons who spend at least $15 during a trip to Springdale Mall / Total number of persons in the survey
= 108 / 150
= .72
b) P(spends at least $15 during a trip to Downtown) =No. of persons who spend at least $15 during a trip to Downtow / Total number of persons in the Survey
=80 / 150
=0.53333
c) P( spends at least $15 during a trip to West Mall) = No. of persons who spend at least $15 during a trip to West Mall / Total number of persons in the Survey
=78 / 150
=0.52
On Spends, the rank of Springdale Mall is 1, the rank of Downtown is 2, the rank of Westmall 3.
d) P(Feels that Springdale Mall has the highest-quality goods) = No. of Persons who feels that Springdal Mall has the highest-quality goods / Total number of persons in the survey
= 80 / 150
= 0. 533333
e) P(feels that Downtown has the highest-quality goods) = No. of Persons who feel that Downtown has the highest-quality goods / Total number of persons in the survey
= 36 / 150
= 0. 24
f) P(feels that West Mall has the highest-quality goods) =No. of Persons who feel that West Mall has the highest-quality goods / Total number of persons in the survey
= 15 / 150
= 0. 1
On heighest-quality goods, the rank of Springdale Mall is 1, the rank of Downtown is 2, the rank of Westmall 3.
g) P(that she spends at least $15 during a trip to Springdale Mall) = No. of females who spends at leat $15 during a trip to springdale Mall / Total no. person in the survey
=111 / 150 = 0. 74
Males are less likely than a female to spend at least $15 during a visit to this area.
h) P(that she spends at least $15 during a trip to Downtown) = No. of females who spends at leat $15 during a trip to Downtown / Total no. person in the survey
= 124 / 150 = 0. 82666
Males are less likely than a female to spend at least $15 during a visit to this area.
i) P(that she spends at least $15 during a trip to Westmall) = No. of females who spends at leat $15 during a trip to West mall / Total no. person in the survey
= 36 / 150 = 0. 24
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.
