Pierced Jeans is a clothing retailer, known for its high-tech performance evaluation techniques (used to assess and reward its sales-staff). PJ’s has shared in-store transaction records for 1090 transactions (see file pjsales). Each transaction is defined as the entrance of a customer into the store and records the following information: who was the salesperson, whether the potential sale successful (Y/N), and whether transaction was during a daytime or an evening shift.
QUESTIONS
1. Identify the variables represented in this data set, being sure to note whether each variable is qualitative (i.e., categorical) or quantitative.
2. How many salespersons are represented in this data set? We refer to this as the number of levels attributed to the categorical variable (or factor).
3. Construct a contingency table to summarize the distribution of transactions by sales-
person (Alphonse, Belinda) and by success (Y, N). Please include the margins in your
table.
a) First express the contingency table as a frequency table (in terms of
counts)
b) Reproduce the table only this time in terms of relative frequency
c) Zihan, PJs chief data analyst, has randomly chosen one transaction from the data set represented by the contingency table above (i.e., part b). Please calculate the following.
i. The probability that the transaction is attributed to Alphonse or represents a successful sale attributed to Belinda.
ii. Zihan informs you that the transaction represents a successful sale. Calculate the probability that the sale was made by Belinda.
4. Using an appropriate display compare the number of successful sales between salepersons
a) First plot a graph that ignores (is unconditional upon) shift
b) Now repeat your analysis (from part (a)) but conditioning on each of the
levels for shift, i.e., repeating the analysis for only daytime and then for only evening shifts. Please display these plots in terms of relative frequencies (proportions)
c) Please contrast the conclusions one might draw when conditioning your analysis upon shift versus the original marginal analysis (i.e., when you ignored shift).
5. Assume 10 customers arrive under the scenarios described below (you may assume that the event of a successfull sale is independent from one customer/transaction to the next).
What is the probability of at least one sale for each of the following scenarios (hint: use the appropriate relative frequency data as an estimate for appropriate probabilities):
(a) When Alphonse is the salesperson during an evening shift
(b) When Belinda is the salesperson during an evening shift
(c) When Belinda is the salesperson during a daytime shift
(d) Comment on how the numeric results for these three scenarios compare.
6. Consider a daytime scenario where each salesperson faces one transaction each, and assume that their probabilities of success are independent of one and another. Answer the following (i.e., you may use the daytime proportions of success sales (out of transactions) for each salesperson as his/her probability of success):
(a) What is the probability that either salesperson makes a sale?
(b) What is the probability that neither makes a sal
