Analytic Exercise - Jimmy Quickfingers and Control Limits

Reference no: EM132400906

Analytic Exercise - Jimmy Quickfingers and Control Limits

Recall from lecture that Caesar's Palace is investigating its dealer Jimmy Quickfingers due to an abnormally bad month: an average loss of $12,000 per night at his table over 20 nights.

Caesar's asks you to provide consulting services. They provide you with the average nightly earnings at its tables among dealers who are known to be honest ($60,000) and the standard deviation of nightly earnings ($100,000).

1. Is this enough information for you to specify how average monthly earnings are distributed? If so, explain why and provide the distribution in words, symbols, and in a figure. If not, explain why not.

2. Explain why it is important that the statistics given to you by Caesar's are known to come from honest dealers.

3. You suggest that the proper strategy for evaluating Jimmy's performance is not to dangle him over a shark tank (as your clients suggest), but instead to set control limits based on company data. You ask Caesar's how costly for them to keep a cheating dealer relative to firing a good, honest dealer incorrectly. They cannot provide you with specific data, but they say that a cheater is extremely costly to them, as s/he creates a culture of further cheating. Given this information, would you set the rate of Type I error at 1%, 5%, or 10%? Explain.

4. Given your answer to part (3), calculate the control limits.

a. First, note how many standard errors away from the mean you wish to set the upper and lower bounds.

b. Then, apply this number of standard deviations to the distribution of the sample mean you care about. Where are the control limits? Draw the distribution of the sample mean indicating the control limits. Shade the areas "outside" the control limits. What do these areas represent?

c. Do you recommend that Caesar's fire Jimmy? How many standard errors away from the mean was Jimmy's month?

5. Suppose personnel are evaluated every month.

a. Intuitively, how likely does a Type I error become over long periods of time? What does that imply for how you should set control limits (or other personnel policy) with "multiple testing"?

b. If you set the rate of Type I error equal to 0.001 (that is, 0.1%), what is the rate of Type I error in a set of 100 independent tests? How about 1000 tests?

Reference no: EM132400906

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