Introduction
This is a probability analysis paper that is based on the results of a telephone survey that was conducted to determine the strengths and weaknesses of Springdale, Downtown and West malls located in Springdale. There were 150 respondents and 30 variables in the survey. The paper concentrates on 8 variables.Q1
- There were 107 respondents who stated that they spend at least $ 15 dollars during a trip to Springdale Mall. Therefore, the probability that a randomly selected respondent spends at least $ 15 to shop at Springdale Mall is 107/150 which translates to 0.71. Probability is computed by dividing the number of favorable outcomes by the number of possible outcomes (Courgeau, 2012).
- There were 84 respondents who stated that they spend at least $ 15 dollars during a trip to Downtown. Therefore, the probability that a randomly selected respondent spends at least $ 15 to shop at Downtown is the probability is 84/150 which translates to 0.56.
- There were 80 respondents who stated that they spend at least $ 15 dollars during a trip to West Mall. Therefore, the probability that a randomly selected respondent spends at least $ 15 to shop at West Mall is 80/150 which translates to 0.53.
Shoppers are more likely to spend at least $15 dollars at Springdale Mall Downtown and West Mall. Consequently, Springdale is the strongest mall in terms of amount of money a shopper spends during a typical shopping visit. West Mall is the weakest.
- There were 79 respondents who felt that Springdale Mall had the highest quality of goods. Therefore, the probability that a randomly selected respondent feels that Springdale Mall has the highest quality goods is 79/150 which translates to is 0.53.
- There were 38 respondents who felt that Downtown had the highest quality of goods. Therefore, the probability that a randomly selected respondent feels that Downtown has the highest quality goods is 38/150 which translates to is 0.25.
- There were 11 respondents who felt that West Mall had the highest quality of goods. Therefore, the probability that a randomly selected respondent feels that West Mall has the highest quality goods is 11/150 which translates to is 0.07.
The Springdale Mall is the strongest in terms of the quality of goods offered while West Mall is the weakest. Springdale and West Mall had the highest and the lowest probability respectively.
Q2.
The above is a contingency table used for calculation of the probabilities. A contingency table contains the counts or frequency of outcomes (Agresti, 2002). There were 86 female respondents. 65 female respondents stated that they spend at least $15 during a trip to Springdale Mall. Therefore, the probability that a randomly selected respondent is a female and spends at least $15 to shop at Springdale is given by the product of 86/150 and 65/86 which translates to 0.43. The two probabilities are dependent. Product is used when the probability that a randomly selected respondent is a male and spends and spend at least $15 is 0.28. Therefore females are more likely spend at least $15 during a visit to Springdale.
There were 86 female respondents. 43 female respondents stated that they spend at least $15 during a trip to Downtown. Therefore, the probability that a randomly selected respondent is a female and spends at least $15 to shop at Downtown is given by the product of 86/150 and 43/86 which translates to 0.29. The probability that a randomly selected respondent is a male and spends and spend at least $15 is 0.27. Therefore females are more likely spend at least $15 during a visit to Downtown.
There were 86 female respondents. 50 female respondents stated that they spend at least $15 during a trip to West Mall. Therefore, the probability that a randomly selected respondent is a female and spends at least $15 to shop at West Mall is given by the product of 86/150 and 50/86 which translates to 0.33. The probability that a randomly selected respondent is a male and spends and spend at least $15 is 0.20. Therefore females are more likely spends at least $15 during a visit to West Mall.
Conclusion
The residents of Springdale are more likely to spend $15 dollars or more during their visit to Springdale Mall than any other Malls; Downtown and West. Again, majority of the resident feel that Springdale Mall offered the highest quality of goods. More females than males are more likely to spend $ 15 or more at all the malls.
References
Agresti, A. (2002). Categorical data analysis. New York: Wiley-Interscience.
Courgeau, D. (2012). Probability and social science: Methodological relationships between the two approaches. Dordrecht: Springer.
