# Probability

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**Option 1: 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 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.

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Order Paper NowThe 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. Do not convert to percentages as we are interested in probabilities only here.

- Based on the relative frequencies for responses to each variable, determine the probability that a randomly selected respondent from:
- SPRSPEND [variable 4] spends at least $15 during a trip to Springdale Mall.
- DOWSPEND [variable 5] spends at least $15 during a trip to Downtown.
- WESSPEND [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:
- BSTQUALI [variable 11] feels that Springdale Mall has the highest-quality goods.
- BSTQUALI [variable 11] feels that Downtown has the highest-quality goods.
- BSTQUALI [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:
- SPRSPEND and RESPGEND [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?
- DOWSPEND and RESPGEND [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?
- WESSPEND and RESPGEND [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.

**Paper Requirements**

Write a report that uses the *Written Assignment Requirements* under the heading *Expectations for CSU-Global Written Assignments* found in the CSU-Global Guide to Writing and APA. Items that should be included, at a minimum, are a title page, an introduction, a body which answers the questions posed in the problem, and a conclusion paragraph that addresses your findings and what you have determined from the data and your analysis. As with all written assignments, you should have in-text citations and a reference page. Please include any tables of calculations, calculated values, and graphs associated with this problem in the body of your assignment response.

Note: You *must* submit your Excel file with your report. This will aid in grading with partial credit if errors are found in the report.

**Option 2: Probabilities of Graduation and Publication**

**Instructions**

In the following study, three different universities have been tracking a select group of professors over the course of their employment at that university to determine the number of students who are in a particular professor’s classes, how many of those students have graduated, and if any of them have had their work published. In the attached Excel file, Probabilities, are the totals for each of the professors at the three different universities that participated in the study.

The purpose of this study is to find the probabilities of graduation and publication for the students in the different professors’ courses. While a causal relationship may not be found between a professor and student graduation or publication, we need to rank the professors based on the different probabilities found with the data sets as described below.

Prepare a report (see below) with your ranking of the professors based on the probabilities and conditional probabilities as well as the analysis of each university. Include the following seven (7) items in table format which is provided in the Probabilities file to support your ranking.

Note: Be sure to use five (5) decimal places for your probabilities in the table, as some of them will be quite small. Do not convert to percentages as we are interested in probabilities only here.

- The overall probability of students graduating at each of the three universities.
- The overall probability of students having a publication at each of the three universities.
- The overall probability of students having a publication, given that they graduated at each of the three universities.
- The probability of a student graduating for each professor.
- The probability of a student having a publication for each professor.
- The probability of a student having a publication given that they graduated for each professor.
- Rank the professors within each university for each of the probabilities in 4–6. Then find the sum of the ranks and determine an overall ranking for each professor.

Be sure to critically analyze the above calculations in your body paragraphs, explaining how you found each type of probability and then the results you obtained. Be sure to also explain your criteria for ranking in steps 4–7, and defend why you chose that ranking method—as your way might not be the typical method.

**Paper Requirements**

Write a report that uses the *Written Assignment Requirements* under the heading *Expectations for CSU-Global Written Assignments* found in the CSU-Global Guide to Writing and APA. Items that should be included, but are not limited Items that should be included, at a minimum, are a title page, an introduction, a body which answers the questions posed in the problem, and a conclusion paragraph that addresses your findings and what you have determined from the data and your analysis. As with all written assignments, you should have in-text citations and a reference page. Please include any tables of calculations, calculated values, and graphs associated with this problem in the body of your assignment response.

Note: You *must* submit your Excel file with your report. This will aid in grading with partial credit if errors are found in the report.