In this paper, we examine the data obtained from the Springdale Shopping Survey. We will create contingency tables and relative frequency probabilities in order to provide the answers to the given questions.These answers will provide helpful insights to the shopping mall management. The variables we choose for this analysis is related to customers’ spending behavior depending on their gender and other significant factors.
So, according to the instructions, the variables participated in this research work are:
Variable # 4: How much the respondent spends during a trip to Springdale Mall?
Variable # 5: How much the respondent spends during a trip to Downtown?
Variable # 6: How much the respondent spends during a trip to West Mall?
Variable # 4: How much the respondent spends during a trip to Springdale Mall?
Variable #11: Which shopping area best fits to the characteristics “high quality of goods”
Variable #26: Information about the Respondent (Gender).
Problem #1
Based on the relative frequencies, determine the probability that a random respondent spends at least $15 during a trip to Springdale Mall.
Create the frequency table for the variable #4:
The probability that a randomly chosen respondent spends at least $15 is equal to 1 minus the probability that he spends less than $15. The probability that he spends less than $15 is 0.31333. Hence, the probability that he spends at least $15 is:
P=1-0.31333=0.68667
Problem #2
Based on the relative frequencies, determine the probability that a random respondent spends at least $15 during a trip to Downtown.
Same procedure here, we create the frequency table for variable #5:
P=1-0.47333=0.52667
Problem #3
Based on the relative frequencies, determine the probability that a random respondent spends at least $15 during a trip to West Mall.
Similarly to problems #1 and #2, create the frequency table for variable #6:
P=1-0.49333=0.50667
According to the results, we can conclude that the areas can be ranked from strongest to weakest in terms of the amount of money a shopper spends during a typical shopping visit in the following way: Springdale Mall, Downtown, West Mall. In other words, respondents spend at least #15 in Springdale Mall (0.68667) most often among the given three areas, next goes Downtown (0.52667) and the last is West Mall (0.50667).
Problems #4-6
Based on the relative frequencies, determine the probability that a random respondent feels that the Springdale Mall (Downtown, West Mall) has the highest-quality goods.
Create the frequency table for the variable #11:
The probability that a randomly chosen respondent feels that the Springdale Mall has the highest-quality goods is 0.52667. Similarly, this probability is 0.24667 for Downtown and 0.07333 for West Mall.
According to the results, the areas can be ranked from strongest to weakest in terms in the quality of goods in the following way: Springdale Mall, Downtown, West Mall.
Problem #7
Set up a contingency table for the variables gender and spends in the Springdale Mall to find the following probability: given that the random respondent is a female, what is the probability that she spends at least $15?
The probability that female spends at least $15 is:
P=6689=0.74157
The probability that male spends at least $15 is:
P=3761=0.60656
A male is less likely than a female to spend at least $15 in this shopping area.
Problem #8
Set up a contingency table for the variables gender and spends in the Downtown to find the following probability: given that the random respondent is a female, what is the probability that she spends at least $15?
The probability that female spends at least $15 is:
P=4389=0.48315
The probability that male spends at least $15 is:
P=3661=0.59016
A male is more likely than a female to spend at least $15 in this shopping area.
Problem #9
Set up a contingency table for the variables gender and spends in the West Mall to find the following probability: given that the random respondent is a female, what is the probability that she spends at least $15?
The probability that female spends at least $15 is:
P=4889=0.53933
The probability that male spends at least $15 is:
P=2861=0.45901
A male is less likely than a female to spend at least $15 in this shopping area.
According to the results, the shopping areas can be ranked for females as follows: Springdale Mall, West Mall, Downtown. For males, the ranking is the following: Springdale Mall, Downtown, West Mall.
