Economics 310 Menzie D. Chinn Spring 2004 Social Sciences 7418 University of Wisconsin-Madison Final Exam Answer all questions in the 3 (three) bluebooks provided. Make certain you write your name, your student ID number, and your TA’s name on all your bluebooks, as well as noting the bluebook (A, B, or C). Point allocations are proportional to time allocations. Partial credit will be awarded if the written material indicates understanding of how to answer the question (i.e., gibberish will not be given credit). Bluebook A: 24 minutes, hypothesis testing A.1 (10 minutes total) Suppose your firm has been experimenting with two different physical arrangements of its assembly line. It has been observed that both arrangements yield approximately the same average number of finished units per day. To obtain greater process control, you suggest that the arrangement with the smaller variance in the number of finished units per day be permanently adopted. Two independent random samples yield the results shown in the table. Assembly Line 1 Assembly Line 2 1x =85 2x =87 n1=21 n2=21 s21=1200 s22=3600 a) (6 minutes) Conduct a test to determine if the variation in the number of finished units per day for assembly line 1 is less than the number of finished units per day for assembly line 2. Use α= .025. b) (4 minutes) Given the information provided above, is it possible to formally test if the average number of finished units per day for assembly line 1 is the same as the average number of finished units per day for assembly line 2? If yes, how? If no, why? (Hint: what assumptions do you need to test this hypothesis?) A.2 (6 minutes) Smoke detectors are highly recommended safety devices for early fire detection in homes and businesses. It is vital that the devices be nondefective. Suppose 100 Brand A detectors are tested and 12 fail to emit a warning signal. Subjected to the same test, 15 out of 90 Brand B detectors fail to operate. Create a 95% confidence interval to estimate the difference in the fractions of defective smoke detectors produced by the two companies. A.3 (8 minutes) Two surgical procedures are widely used to treat a certain type of cancer. To compare the success rates of the two procedures, random samples of the two types of surgical patients were obtained and the numbers of patients who showed no recurrence of the disease after a 1-year period were recorded. The data are shown in the table.2 Sample size Number of Successes Procedure A 100 78 Procedure B 100 87 Show how to calculate the test statistic for H0: PA - PB = 0. Suppose the p-value for the test was reported as p = .0475. State the proper conclusion when testing Ha: PA - PB < 0 at α = .05. Bluebook B: 36 minutes, regression Consider the following regression results for a regression of the annualized quarterly growth rate of the value of the dollar against the euro (GROWTH_DOLLAREURO) on the difference in the annualized growth rates of US and European labor productivity (GROWTH_USEUPRODDIF). Dependent Variable: GROWTH_DOLLAREURO Method: Least Squares Date: 04/29/04 Time: 21:08 Sample(adjusted): 1989:4 2001:4 Included observations: 49 after adjusting endpoints Variable Coefficient Std. Error t-Statistic Prob. C 0.024188 0.025156 0.961538 0.3412GROWTH_USEUPRODDIF 1.918305 0.894341 2.144936 0.0372R-squared 0.089161 Mean dependent var 0.037881Adjusted R-squared 0.069781 S.D. dependent var 0.176599S.E. of regression 0.170326 Akaike info criterion -0.662240Sum squared resid 1.363521 Schwarz criterion -0.585023Log likelihood 18.22488 F-statistic 4.600749Durbin-Watson stat 1.592695 Prob(F-statistic) 0.037157Note: A 10% growth rate is expressed as 0.10 in the data. a) (4 minutes) Show how to calculate the S.E. of regression using the output above. b) (5 minutes) If the GROWTH_USEUPRODDIF was -1% (that is European productivity is faster than US productivity by 1 percentage points), what would your predicted individual value of the growth rate of the value of the dollar be? What would your estimated mean of the growth rate of the value of the dollar be? c) (3 minutes) If you were to estimate two separate 95% confidence intervals for the predicted value and the estimated mean, which one would be wider? Why? Please provide the reasoning to get credit, no actual calculation is required. d) (6 minutes) Suppose you thought that the behavior of the value of the dollar against the euro was systematically different when European Monetary Union was implemented in 1999. Define a variable EMU that takes on a value of 1 when the EMU is in effect, and 0 otherwise, and then run the regression to obtain:3 Dependent Variable: GROWTH_DOLLAREURO Method: Least Squares Date: 04/29/04 Time: 21:11 Sample(adjusted): 1989:4 2001:4 Included observations: 49 after adjusting endpoints Variable Coefficient Std. Error t-Statistic Prob. C 0.005124 0.027864 0.183885 0.8549 GROWTH_USEUPRODDIF 2.301852 1.000194 2.301405 0.0261 EMU 0.116545 0.064722 1.800693 0.0785 EMU*GROWTH_USEUPRODDIF -3.073703 2.252658 -1.364478 0.1792 R-squared 0.155993 Mean dependent var 0.037881 Adjusted R-squared 0.099726 S.D. dependent var 0.176599 S.E. of regression 0.167563 Akaike info criterion -0.656813 Sum squared resid 1.263474 Schwarz criterion -0.502379 Log likelihood 20.09192 F-statistic 2.772360 Durbin-Watson stat 1.572148 Prob(F-statistic) 0.052294 Interpret in words the coefficient on EMU. Is this coefficient estimate statistically significant? e) (6 minutes) What is the effect of a one percentage point increase in the difference in productivity growth rates on the growth rate of the value of the dollar when the EMU is in effect (use a 20% significance level for making your inferences). f) (6 minutes) Draw a diagram showing the regression lines for periods when the EMU is in effect, and when it is not. Indicate the values of the intercepts and slopes for each regression line. [Draw your graph in your bluebook!] g) (6 minutes) How would you assess the overall utility of our model by using an F-test? GROWTH_DOLLAREURO GROWTH_USEUPRODDIF4Bluebook C: 30 minutes, comprehensive C.1 True/False/Explain (10 minutes total) Events G and F are defined on the sample space of the same experiment, with P(G)=0.5, and P(F)=0.4.