The contingency tables and relative frequency probabilities in this exercise are based on the Springdale Shopping Survey database. Data are in the computer file SHOPPING. 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 examines how conditional probabilities related to spending behavior might vary, depending on the gender of the respondent.
1. Based on the relative frequencies for responses to each variable, determine the probability that a randomly selected respondent
a. [variable 4] spends at least $15 during a trip to Springdale Mall.
b. [variable 5] spends at least $15 during a trip to Downtown.
c. [variable 6] spends at least $15 during a trip to West Mall. Comparing the preceding probabilities, which areas seem strongest and weakest in terms of the amount of money a shopper spends during a typical shopping visit?
d. [variable 11] feels that Springdale Mall has the highest-quality goods.
e. [variable 11] feels that Downtown has the highest quality goods.
f. [variable 11] feels that West Mall has the highest quality goods. Comparing the preceding probabilities, which areas are strongest and weakest in terms of the quality of goods offered?
2. Set up a contingency table for the appropriate variables, 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?
Based on the preceding probabilities, at which shopping areas are males and females most likely and least likely to spend $15 or more during a shopping visit?