ISDS 2710
University of Memphis Fall 2012
Friday Assignment
Make up 2 problems. Choose from the following areas:
Medicine Sporting events
University activities Restaurants
Shopping Track and Field

1. Pick one problem for which you wouldn’t mind underestimating the mean. Explain why. Pick some numbers (µ,σ,xbar,n). Discuss how well your sample mean matches the guess. Discuss what you would do next. 2. Pick one problem for which you wouldn’t want to overestimate or underestimate the mean. Explain why. Pick some numbers (µ,σ,xbar,n). Discuss how well your sample mean matches the guess. Discuss what you would do next. 3. For each of your problems, tell the following: 1. The costs of sampling (what has to be done to get a good sample) 2. The costs of overestimating and underestimating the mean (i.e., What is the impact of making a guess and being wrong?)
1. Write the names of the members of your group today.
_______________________ _______________________
_______________________ _______________________
2. Have the GA sign and indicate time of departure
_______________________ _______________________
GA time

1.) Restaurant Managers. The characteristic to be identified include the mean annual salary for the managers. The population will be 2500 managers, from that population we can select a sample of 30 managers. (I will be using the Web file EAI data as a source of information and table 7.2.) Clearly, the time and the cost of developing a profile for 2500 managers will be substantially less for only 30 managers. Give each manager a four digit random number, discard any numbers higher than 2500 and select then select 30 managers.
I am guessing that restaurant managers on average make $50,000. Using the EAI data, the population mean annual salary is (μ= $51,800), the population standard deviation of annual salary is (σ= $4000).
If you overestimated the salary of managers, the actual salary amount would be lower, therefore the company will to have more money. For example if μ= $55,000 and σ= $4000 then the company would have room to give promotions.
If you underestimated the salary of managers, the actual salary amount would be higher, therefore the company will have less money. For example if μ= $50,000 and σ= $4000 then the company would have less money and no room for promotions.
You can also use the point estimator procedure of using the sample of 30 managers. Using the table 7.2; x= $51,814 and s= $3348. Using this method is less time consuming and more accurate.

2. When dealing with problems in Medicine, especially pertaining to it’s effectiveness in treating illness, one would never want to underestimate or overestimate the amount of medicine that is effective in therapeutically treating patients. Take for instance, if an amount is underestimated the result is making a drug that is ineffective. If someone overestimates an amount of drug it can result in a drug that is too strong which could ultimately lead to toxic or deadly effects. µ= 1.5mg ,σ= 3 mg, xbar= 1.25 mg,n= 200
The guess is that the mean effective amount of medicine is 1.5 mg. A sample of 200 samples of pathogens are tested with amounts with a mean of 1.25 mg. 3.a. The cost of sampling would be cheap in comparison to the cost of overestimating or underestimating the mean. If the mean of an effective amount of drug is underestimated, there could be a production of ineffective drugs in which the company would be throwing away money and producing an ineffective product. If they overestimate the amount of effective drug, the company could end up in a financial bind from lawsuits from ill affected consumers.