LIR832-SPRING-2007-problem-set-3

LIR832-SPRING-2007-problem-set-3 - LIR 832: Problem Set #3...

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Page 1 of 6 LIR 832: Problem Set #3 Joint Distributions, Covariance and Correlation Joint distributions are the building blocks of multi-variate statistics. This problem set consists of two problems to provide you with practice with bi-variate distributions. 1. Psychological testing of employees is, of course, has been in vogue for eighty years. It is often the case that different tests produce somewhat different assessments of employee tendencies and abilities. Your fast food franchising firm is concerned about the dependability of employees. There are two well known tests which cover psychological traits associated with dependability. The first test is well established but is expensive (call this test expensive). The second is less well established but costs half as much to administer and score (call is the cheap). You have administered both tests to six individuals and are interested in whether the cheap test produces results similar to that of the expensive test. The tests are scaled differently. The expensive test is scaled from 1to 10 with 1 being “might show up for own funeral” and 10 “more on time than an atomic clock”. The cheap test is scaled from 0 to 100. Again, higher scores indicate greater dependability. The matched test scores are: Person Expensive Test Score Cheap Test Score A2 3 0 B3 3 0 C5 4 0 D4 3 0 E44 0 F67 0 A. Calculate the means, variances and standard deviations for each test. B. Calculate the covariance for each test C. Calculate the correlation for each test Based on your estimates, do you believe that the expensive test and cheap test give similar indications of dependability? Explain your answer.
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Page 2 of 6 2. We are also concerned about employees tendency to anger when under stress and, again, the expensive and cheap test both provide measures of this trait. A low score indicates a fundamentally calm approach to life (lowest possible score corresponds to ‘may become angry if dropped in a deep frier’) while a high score indicates an individual who tends toward anger (highest possible score indicates ‘becomes uncontrollably angry if middle initial is not included when addressed by name’). Only five individuals answered these questions, our data is The matched test scores are: Person Expensive Test Score Cheap Test Score A2 6 B3 5 C4 5 D5 2 E62 As in the last problem, A. Calculate the means, variances and standard deviations for each test.
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LIR832-SPRING-2007-problem-set-3 - LIR 832: Problem Set #3...

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