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Final Exam 2011 Solution.pdf

Final Exam 2011 Solution.pdf - MBA 200S Data and Decisions...

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MBA 200S Data and Decisions Fall 2011 Final Exam Solutions 1. Work and Cognition. It would be an experiment if the retirement ages were randomly assigned to countries, but the retirement age is determined by the society and the same things that determine retirement age might also determine memory, such as general levels of health or nutrition. In other words, even if correlation is demonstrated, causation is not. 2. Acme Stock. A. Acme stock increases by 1.25 percent for every 1.0 percent increase in the market. B. The t-statistic is, b 1 1 se(b 1 ) = 1.25 1.0 0.156 = 1.603. With 166 degrees of freedom, this t-statistic is slightly smaller than the t-value corresponding to p-value of .05. With software it corresponds to p-value = .0554. We cannot reject the null at a 5% significance level. C. There is no collinearity problem. The variance inflation factors are very low here and both of the explanatory variables are statistically significant. D. Negative. The easiest way to answer this question is to construct a path diagram. The partial slopes for the two explanatory variables are revealed in the MRM. The other piece of information comes from comparing the partial slope for “Market” in the two regressions. Notice that the slope becomes smaller after controlling for “High-Low”. This implies that the two explanatory variables are negatively correlated. Consequently, in the SRM the coefficient on “Market” reflects both the positive direct effect and the positive indirect effect (negative*negative=positive).
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3. Knee Surgery. A. The null and alternative hypotheses are H 0 : µ ≥ 50 and H a : µ < 50. As with most business problems it makes sense to set this up as a one-sided test. The default is that the new technique is no better than the old technique. Only in the case in which we have evidence to reject this null, might the company take action, for example, marketing the new technique. B. Type 1 error here is that the surgery isn’t any better than conventional technique but you reject the null and, for example, market the new technique. Type II error is that the new technique is better, but that you fail to reject the null. Both types of errors are costly to the business.
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