Page 1 of 15LIR 832:Mid-term Examination: Fall, 2003Each Problem is worth 20 points. Answer five of the six problems. Problemsshould be answered as thoroughly as you are able. Partial credit on problems is onlypossible if I can locate errors in your calculations; neatness and organization of youranswers is essential Remember, answer only five of the six problems, if you choseto answer all, I will select the five with the lowest scores.1. Employers depend on their supervisors evaluating their subordinates accuratelyas pay increases, promotion and discipline are largely driven by supervisorsviews of their subordinates. For better or worse, a substantial proportion ofsupervisors views are subjective. Further, different supervisors have differentcriteria for evaluation of subordinates. Differences in criteria can lead tosystematic differences in the ratings of subordinates, with predictableconsequences for the subordinates.Take the case of an establishment with 70 employees and two supervisors. Theemployees are divided into two groups of 35. The two groups do similar workunder similar conditions. Supervisors turn in evaluations of all of theirsubordinates each August 31. We are curious about whether our twosupervisors apply our evaluation criteria consistently, so that employees are notdisadvantaged by working for one or the other supervisor. We decide to use thecurrent evaluations to test whether the supervisors are consistent with oneanother (by the way, we have no reason to believe that their employees differ intheir performance in any consistent fashion).A. Calling the first supervisor A and the second supervisor B, set up a nulland alternative hypothesis to test whether the supervisors are different. Isthis a one or two tailed test?Page 2 of 15B. We calculate the mean and standard deviation for each supervisorssubordinates. For supervisor A, the mean of the evaluation is 3.0 with astandard deviation of 1.3; for supervisor B the mean is 3.4 with a standarddeviation of .5. Can you reject the null in a 10% test? A 5% test? A 1%test?C. Explain what it means to reject the null in a 5% test.Page 3 of 152. Safety is an important issue in construction, the industry has one of the highestrates of fatal and non-fatal injuries of any industry in the United States. In someoccupations, such as structural iron work, workers compensation payments canbe equal to payroll.Many consultants offer construction safety programs. One of the more populartypes of programs are group rewards for reducing lost time accidents. Forexample, a program might provide a cash bonus to all workers on a constructionproject if there are no lost time accidents on the project. The evaluations of theeffectiveness of these programs vary. Although the evidence often indicates areduction in the number of injuries on a job site, there is disagreement as to thereduction in whether the number of injuries is reduced or whether workers,seeking the cash rewards, no longer report injuries. The problem of determiningwhether there is a reduction in the number of injuries, or in the reporting ofinjuries, probably does not affect fatal injuries; it is difficult to conceal fatalities.We have information on 27 large scale long term construction projects thatimplemented group rewards safety programs. These projects averaged .75fatalities with a standard deviation of .71. The national average of fatalities forsimilar construction projects is .98.A. Set up the alternative and null hypothesis for testing whether grouprewards programs reduce construction fatalities.B. Using the data provided, test to determine if the null can be rejected in a10%, 5% or 1% hypothesis test. What is your conclusion.Page 4 of 153. It is generally believed that the age of the labor force is positively associated withmedical costs. Medical problems tend to show up as one gets older because ofthe aging process but also because the increased responsibilities that typically gowith getting older (marriage, children, mortgage, etc) tend to reduce the time onecan spend on activities which promote health. We therefore expect olderemployees to be less healthy, use more health care and expend more on healthcare than younger employees.This is, at least, the common view. However, the real ringer in the process ischildren. Children use a lot of health care. From before they are born you startgoing to the doctor. Daycare centers are the plague houses of the 21st centuryand we won’t even talk about broken bones and all that. So its not clear that ifwe remove those who have never had children, that older workers have moremedical expenses.Although this would be best to consider in a data set with ten or fifteen thousandobservations, we are going to use just five observations of individuals ages andmedical expenses. All of the individuals in this data set have at least one child,some of the children may no longer be at home. The data set is:person age prior years medical costs inthousands12852351734722454135625A. Calculate the covariance between age and medical costs. Is the estimateconsistent with the theory that age is positively related to medical costs?(I have laid out a table on the next page to aid in your calculations)Page 5 of 15Page 6 of 15B. Calculate the correlation between age and medical costs. What more doyou learn about this relationship from the correlation than you learnedfrom the covariance?Page 7 of 154. We give an examination every year and over a long time have found that theaverage score is 250 with a standard deviation of 30. Our experience suggestsexam scores are normally distributed.A. What is the probability that an exam taker would score 275 or greater?B. "What is the probability that the average score for 9 individuals taking thetest would be 275 or greater?"Page 8 of 155. Returning to problem three, we remain interested in the relationship between ageand medical expenses. Covariance and correlation only take you so far and wedecide to use regression to estimate the relationship between age and medicalcosts. The data is, again, Person Age Medical Expense in Thousands12852351734722454135625A. Calculate the slope and intercept coefficients using age as theexplanatory variable and prior years medical costs as the dependentvariable. How do you interpret each of these coefficients? (I have laid outa Table on the next page to aid in your calculations)Page 9 of 15Page 10 of 15Page 11 of 15B. What are