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LIR 832:Mid-term Examination: Spring, 2003Each Problem is worth 20 points. Answer five of the six problems. Problems should beanswered as thoroughly as you are able. Partial credit on problems is only possible if I canlocate errors in your calculations; neatness and organization of your answers is essentialRemember, answer only five of the six problems, if you chose to answer all, I will select thefive with the lowest scores.1. A random variable X is normally distributed. What is the probability of observing avalue of X such that:a. X > 220 where X has a mean of 200 and a variance of 144b. X < -25 where X has a mean of -10 and a variance of 121c. 1510 < X < 1535 where X has a mean of 1520 and a variance of 49d. X > 2000 or X < -1000 where X has a mean of 500 and a variance of 225e. .0012 > X > .0009 where X has a mean of .001 and a variance of .0001962. A consultant is peddling a program which she promises will increase the productivity ofour employees. The premise of the program is that when communication between plantmanagement and employees is not good employees feel little attachment or loyalty to thefirm. The program aims to improve communication by increasing the contact betweenplant management, clericals and production employees through structured informalinteractions: management walk arounds, meetings between employees and managers andeven some dinners in which plant managers host small groups of employees.An acquaintence of yours has tried this program at six of her plants (these were chosenby random sampling from her thirty plants. All plants are identical and should producethe same dollar value per employee). Three of the plants were controls, no change wasmade in managerial/employee interaction; three of the plants implemented this program. We have data on the percentage of employees who met with plant management for atleast an hour over the last month and the dollar value of output in the following monthPercent Meeting Management Value of Output per Employeeplant 1 10 100plant 2 15 95plant 3 13 107plant 4 55 105 plant 5 65 93plant 6 85 115Percent meeting management is the percent of employees who met managementin the prior month. Value of output per employee is the dollar value of output inthe plant in the current month divided by the number of employeesa. Calculate the mean and standard deviation of each variable, their covariance andcorrelation. Do these results validate the consultants claim? Explain youranswer.(There are two blanks pages at the end of this problem for calculations)(Continued on the next page)b. Its nice to have covariances and correlations, but regression coefficients wouldtell us more about the relationship between meetings and output. Calculate theslope coefficient and intercept for the effect of meetings (X) on the value ofoutput (Y).c. What is the estimated effect of a 1 percentage point increase in meeting time onoutput? How do we interpret the intercept?(Continued on the next page)d. What is r2 for this equation?3. Health care costs are currently rising between ten and twelve percent per year and this isplacing considerable strain on the health care system in the United States. The increase incost is affecting employers ability to provide both health insurance and pay increases. There are newspaper stories about substantial numbers of employers shifting the costs ofhealth care onto their employees as well as stories about employers dropping healthinsurance cover for their employees.a. Using data from the 2000 U.S. Census, we find that the typical employee paid $55per month for their employer provided health insurance. A 2004 national surveyof 100 employees found that, on average, employees paid $66 per month forhealth insurance with a standard deviation of $63. Construction a hypothesis testto determine whether employees are paying more for health insurance than theydid in 2000. Can the null be rejected in a 10%, 5% or a 1% test?b. Using the same two sources of data we find that 64.5 percent of U.S. employeeshad employer based coverage in 2000, but that this has declined to 56.4 percent inour current sample. The standard deviation of the sample is 35. Test whetherhealth insurance coverage has declined using a 10%, 5% and 1% test.4. Calculate the means, variances, standard deviations and covariance and correlation for X & Y. The probabilities for the jointdistribution of X and Y are in the body of the table.Y05 1010 0.1 0.1 0.2X15 .30 0.2. 0.120 .2 0 0.15. You have recently been hired into a HR position at the Peter Gibbons Word ProcessingCompany. As one of your first tasks, you are asked to review a productivity study ofyour word processing staff by an HR consultant. As part of this study, he as estimatedthe regression:Words Typed = 35 + 3*(Education) + 5*(Typing Classes Taken) – 2*(Age)R2 = .31 R230=.Where:Words Typed = Words typed per minuteEducation = Years of education completedTyping Classes Taken = The number of typing classes completedAge = Age in yearsa. Interpret each of the three slope coefficients, remembering that magnitude mattersas well as sign.b. Comment on the intercept – what does it mean? How should this be interpreted? c. What do the R-squared and R-bar-squared values mean about the regression?d In the appendix of the consultant’s report, the consultant includes a secondestimated productivity equation. This equation is Words Typed = 25 + 1*(Education) + 8*(Typing Classes Taken) – 1*(Age) - 3*(# reprimands by supervior)R2 = .33 R229=.The consultant claims that this equation is not as good as the first equation. Doyou agree with him? Explain your answer accounting for all of the applicableinformation.6. During a stop on his campaign tour in Lansing, congressional candidate SpendmoreIgnoramus proclaims that Ingham County garbage collectors make $1000 a week. SinceMr. Ignoramus has been prone to speak untruths, we believe that such garbage collectorsdo not make such a weekly salary. Since we don’t have any readily-available statistics on the weekly salaries of garbagecollectors, we decide to ask our local collector, Dennis Debris, about his weeklypaycheck. He suggests that he, in fact, makes $855 per week. And from prior research,you know that the standard deviation in $100. a. Thus, given our one observation, construct a hypothesis test of your beliefregarding Mr. Ignoramus’ statement, and test it at a 10%, 5% and 1% test ofsignificance. What do you


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