# LIR 832 Fall-2004-midterm-examination-answer-key - LIR 832...

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Page 1 of 11 LIR 832: Mid-term Examination: Fall, 2004 Each Problem is worth 20 points. Answer five of the six problems. Problems should be answered as thoroughly as you are able. Partial credit on problems is only possible if I can locate errors in your calculations; neatness and organization of your answers is essential Remember, answer only five of the six problems, if you chose to answer all, I will select the five with the lowest scores.

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Page 2 of 11 1. Employers depend on their supervisors evaluating their subordinates accurately as pay increases, promotion and discipline are largely driven by supervisors views of their subordinates. For better or worse, a substantial proportion of supervisors views are subjective. Further, different supervisors have different criteria for evaluation of subordinates. Differences in criteria can lead to systematic differences in the ratings of subordinates, with predictable consequences for the subordinates. Take the case of an establishment with 70 employees and two supervisors. The employees are divided into two groups of 35. The two groups do similar work under similar conditions. Supervisors turn in evaluations of all of their subordinates each August 31. We are curious about whether our two supervisors apply our evaluation criteria consistently, so that employees are not disadvantaged by working for one or the other supervisor. We decide to use the current evaluations to test whether the supervisors are consistent with one another (by the way, we have no reason to believe that their employees differ in their performance in any consistent fashion). A. Calling the first supervisor A and the second supervisor B, set up a null and alternative hypothesis to test whether the supervisors are different. Is this a one or two tailed test? let be ervisor A s mean population rating similar for ervisor B then Hi s o r s o r these are two tailed tests A oAB A B AAB A B µ µµ sup ' , sup . . =− = ≠− 0 0 B. We calculate the mean and standard deviation for each supervisors subordinates. For supervisor A, the mean of the evaluation is 3.0 with a standard deviation of 1.3; for supervisor B the mean is 3.4 with a standard deviation of .5. Can you reject the null in a 10% test? A 5% test? A 1% test? σ AB z =+ = = = 13 35 5 35 22 2354 34 30 2354 16999 .. . . . As this is a two tailed test, our p-value for the null is .0446*2 or 8.92%. So we can reject in a 10% test but not a 5% or 1%. Alternatively, our cut points for a two tailed with a large sample would be 1.645 (10%), 1.96 (5%) and 2.576(1%). 1.699 is barely larger than the 10% cut point, and isn’t larger than the 5% or 1%.
Page 3 of 11 C. Explain what it means to reject the null in a 5% test. When we say we can reject in a 5% test, what we mean if that “if the null were true, we would expect to see a sample mean as extreme - - as far from the mean assumed in the null - - in no more than 5 out of 100 samples.

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LIR 832 Fall-2004-midterm-examination-answer-key - LIR 832...

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