Reference no: EM132378033

ADM 2303 - Statistics for Management

Assignment

PJam Jeans (PJamJs) is a clothing retailer, known for its performance evaluation techniques (used to assess and reward its sales-staff). PJamJ’s has shared in-store transaction records for 1000 transactions (see file pjamjsalesy19.). 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 was successful (Y/N), and whether transaction was during a daytime or an evening shift.

Please answer the following questions in regards to this dataset.

QUESTIONS

1. Identify the variables represented in this dataset, being sure to note whether each variable is qualitative (i.e., categorical) or quantitative.

2. How many salespersons are represented in this dataset? We refer to this as the number of levels attributed to this categorical variable (aka, factor).

3. Construct a contingency table to summarize the distribution of transactions by salesperson (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 (i.e., proportions vis a vis the total, rather than row-totals or column-totals)

(c) Zihan, PJamJs chief data analyst, has randomly chosen one transaction from the dataset represented by the contingency table above (i.e., part b). Please calculate the following.

i. The probability that the transaction is attributed to Alphonse (regardless of success) or represents an unsuccessful sale for Belinda.

ii. Zihan informs you that the transaction represents a unsuccessful sale. Calculate the probability that the sale was made by Belinda.

4. Using an appropriate display compare the success rate between salespersons (hint. A salesperson will have at most as many successes as they have transactions. So if a different employee, say Jennifer, was on the job for 40 transactions, and 32 of those were successes, then her success rate would be calculated as 32/40; dividing instead by the total number of transactions available to all salespersons would be unhelpful.)

(a) First plot a graph that ignores (is unconditional upon) shift (b) (4 points) 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. 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 of at least one successful sale?

(b) What is the probability that neither makes a sale.

6. PJamJ Management informs you that the data provided were collected as part of a study investigating the potential gains in success-rate induced by exposing a salesperson to a check-list — the study involved exposing each salesperson to the check-list before his/her night shift.

PJamJ Management would like you to estimate the beneficial effect of this checklist intervention — namely by quantifying what the success rate would have been in the absence of the checklist exposure, and noting what improvement the exposure induced. Can this be estimated? Why or why not?