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 150 respondents were also asked to provide information about themselves and their shopping habits. The data are provided in the file SHOPPING. The variables in the survey can be found in the file CODING.

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.

1. Based on the relative frequencies for responses to each variable, determine the probability that a randomly selected respondent from

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, rank the areas from strongest to weakest in terms of the amount of money a shopper spends during a typical shopping visit.

2. Based on the relative frequencies for responses to each variable, determine the probability that a randomly selected respondent from

a. [variable 11] feels that Springdale Mall has the highest-quality goods.

b. [variable 11] feels that Downtown has the highest-quality goods.

c. [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.

3. Set up a contingency table for the appropriate variables given, 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?

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.

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