Answer all five questionsNov. 1, 2001 ECON 240A-1 L. PhillipsMidtermAnswer all five questions1. (15 points) All printed circuit boards (PCBs) that are manufactured at a certain plant are inspected for flaws. Experience has shown that 50% of the PCBs produced are flawed in some way. Of the flawed PCBs, 60% are repairable, while the remainder are seriously flawed and must be discarded. A newly manufactured PCB is selected before undergoing inspection. What is the probability that it will not have to be discarded? 2. (15 points) Mensa is an organization where members possess IQ’s in the top 2% of the population. a. If IQ’s are normally distributed, with a mean of 100 and a standard deviation of 16, what is the minimum IQ necessary for admission?b. If three individuals are chosen at random from the general population, what is the probability that all three satisfy the minimum requirement for admission toMensa?3. (15 points) Determine the sample size needed to estimate a sample proportion with a 95 % confidence interval for its expected value of plus or minus 0.03, givena. a sample proportion on the order of 0.05.b. a sample proportion on the order of 0.5.c. What distribution did you use in your calculations. 4. (15 points) The following graph 4-1 shows the results of regressing California General Fund expenditures, in billions of nominal dollars, against California PersonalIncome, in billions of nominal dollars beginning in fiscal year1968-69 and ending in fiscal year 2001-02. a. How much of the variance in the dependent variable is explained by personal income?b. Interpret the estimated slope. Table 4-1 follows with the estimated parameters and table of analysis of variance.c. Is the slope significantly different from zero? What statistic do you use to answer this question? What distribution do you use to answer this question? What probability were you willing to accept for a Type I error?Nov. 1, 2001 ECON 240A-2 L. PhillipsMidtermd. What is the ratio of the explained mean square to the unexplained mean square?Figure 4-1: California General Fund Expenditures Versus California Personal Income, both in Billions of Nominal DollarsTable 4-1: Summary OutputRegressionStatisticsMultiple R 0.9904673R Square 0.9810255Adjusted R Square 0.9804325Standard Error 2.9988336Observations 34ANOVAdf SS MS F SignificanceFRegression 1 14878.68965 14878.69 1654.47398 3.98668E-29Residual 32 287.7761003 8.993003Total 33 15166.46575CoefficientsStandard Error t Stat P-value Lower 95% Upper 95%Intercept -1.197411 0.927956018 -1.29037 0.20616709 -3.08759378 0.6927721X Variable 1 0.0659894 0.001622349 40.67523 3.9867E-29 0.062684796 0.069294Calfifornia General Fund Expenditures Vs. California Personal Income, Billions of Nominal $y = 0.066x - 1.1974R2 = 0.98101020304050607080900 200 400 600 800 1000 1200 1400Personal IncomeGen Fund ExpendituresNov. 1, 2001 ECON 240A-3 L. PhillipsMidterm5. (15 points) The following graph 5-1 shows the results of regressing the logarithm of California General Fund Expenditures (in billions of nominal dollars) against the logarithm of California Personal Income (in billions of nominal dollars).a. How much of the variance in the dependent variable is explained by the independent variable?b. Interpret the estimated slope.c. Express the fitted equation in terms of the variables: California General Fund Expenditures (fitted) and California Personal Income.Figure 5-1: The Logarithm of California General Fund Expenditures Versus the logarithm of California Personal Income, both in Billions of Nominal DollarsTable 5-1 follows with the estimated parameters.d. Test the hypothesis that the slope equals one.e. What is the economic/political significance of this hypothesis test?The Logarithm of California General Fund Expenditures Vs. The Logarithm of California Personal Income, Billions of Nominal Dollarsy = 0.0398x1.0737R2 = 0.987711010010 100 1000 10000CA Personal IncomeCA Gen Fund ExpendituresNov. 1, 2001 ECON 240A-4 L. PhillipsMidtermTable 5-1: Variable Coefficient Std. Error t-Statistic Prob. LNPERSINC 1.073723 0.021175 50.70825 0.0000C -3.224482 0.125736 -25.64487 0.0000R-squared 0.987708 Mean 3.091322Adjusted R-squared 0.987324 S.D. 0.891602S.E. of regression 0.100384 Akaike -1.702610Sum squared resid 0.322461 Schwarz -1.612824Log likelihood 30.94437 F-statistic 2571.327Durbin-Watson stat 0.347529 Prob(F- 0.000000Figure5-2 follows.f. Is there any evidence of multicollinearity? Why or why not?g. Is there any evidence of autocorrelation? Why or why not-0.2-0.10.00.10.20.31234570 75 80 85 90 95 00Residual Actual FittedFigure 5-2: Plot of Actual, Fitted and Residuals for the Logarithm of California General Fund Expenditures Regressed on the Logarithm of California Personal
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