3. The manager of an ice cream parlor located in a small resort town is trying to decide whether or not to purchase a new soft serve machine. The new equipment will cost $3,200 or $3.2k. The profitability of this investment will depend on whether the vacation season is booming or slow. There is a 15% probability the vacation season will be slow. The table below shows expected profits, in thousands, for the various vacation season and machine purchase combinations. These numbers do not factor in the cost of the new machine.

Using the methodology demonstrated in QuAC, answer the following questions. Show all of your work:

 What decision should the manager make using EMV as her criteria?

 The manager is not confident that the probability of a slow vacation season is 15%. At what probability level will she change the decision she made above, under EMV?

 The manager is also not confident about the $27k she estimates as profit if the machine is purchased and the vacation season is booming. At what profit level will she change her decision from that made under EMV?

Employee Retention

Demand for systems analysts in the consulting industry is greater than ever. Graduates with a combination of business and computer knowledge—some even from liberal arts programs— are getting great offers from consulting companies. Once these people are hired, they frequently switch from one company to another as competing companies lure them away with even better offers. One consulting company, D&Y, has collected data on a sample of systems analysts they hired with an undergraduate degree several years ago.

The variables are:

D&Y is trying to learn everything it can about retention of these valuable employees. You can help by solving the following problems and then, based on your analysis, presenting a report to D&Y. To begin, use the appropriate summary measures to describe the pool of system analysts.

Develop a 95% confidence interval around starting salary. As can be seen, starting salaries are in a fairly narrow band; D&Y wonders whether they have anything to do

with retention.

Use confidence intervals to estimate the proportion of employees who stay with D&Y for at least 3 years. If you divide your sample into two, by separating at the mode starting salary, does this proportion change as you look at employees below the mode and employees above the mode? Perform the necessary hypothesis tests to investigate and comment on your findings.

Is there a difference in salary between employees who stay at least 3 years with D&Y those who leave before 3 years? Perform the necessary hypothesis tests to investigate and comment on your findings.

D&Y wonders whether the percentage of time on the road might influence who stays and who leaves. Use confidence intervals to estimate the mean percentage of time on the road. If you divide your sample into two, by separating at the mode starting salary, does this percentage change as you look at employees below the mode and employees above the mode? Perform the necessary hypothesis tests to investigate and comment on your findings.

State University ’s students, particularly those in its nationally acclaimed CIS area, have traditionally been among the best of D&Y’s recruits. But are they relatively hard to retain? Estimate (to 95% certainty) the mean starting salary of employees from State U. Repeat the analysis for employees with a CIS degree. Compare this estimate to an estimate of the mean starting salary of employees that are not from State U. and without a CIS degree. Is there a difference? Perform the necessary hypothesis tests to investigate and comment on your findings. Are there any other differences between employees that are or are not from State U. or with and without at CIS degree?

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