Answer all five questionsTablePlotTablePlotNov. 2, 2000 ECON 240A-1 L. PhillipsMidtermAnswer all five questions1. (15 points) Approximately three out of four Americans who filed a 1995 tax return received a refund. If three individuals are chosen at random from among those who filed a 1995 tax return, find the probabilities of the following events.a. All three received a refundb. None of the three received a refund.c. Exactly one received a refund.2. (15 points) For the test of the hypothesis,H0 : = 1000Ha : 1000Given = 0.05, = 200, n = 100a. Find when = 9003. (15 points) A certain city has one morning newspaper and one evening newspaper. It is estimated that 20% of the city’s households subscribe to the morning newspaper and 60% subscribe to the evening paper. Of those who subscribe to the morning paper, 80% also subscribe to the evening paper. a. What proportion of households subscribe to both papers?b. What proportion of households subscribes to at most one of the papers?c. What proportion of households subscribes to neither paper?4. (15 points) The following table shows the results of regressing the natural logarithm of California General Fund expenditures, in billions of nominal dollars, against year beginning in 1968 and ending in 2000. A plot of actual, estimated and residual values follows.a. How much of the variance in the dependent variable is explained by trend?b. What is the meaning of the F statistic in the table? Is it significant?c. Interpret the estimated slope.d. If General Fund expenditures was $68.819 billion in California for fiscal year 2000-2001, provide a point estimate for state expenditures for 2001-2002.e. A state senator believes that state expenditures in nominal dollars have grown over time at 7% a year. Is the senator in the ballpark, or is his impression significantly below the estimated rate, using a 5% level of significance?Nov. 2, 2000 ECON 240A-2 L. PhillipsMidtermf. If you were an aide to the Senator, how might you criticize this regression? TableDependent Variable: LNGENFNDMethod: Least SquaresSample: 1968 2000Included observations: 33Variable Coefficient Std. Error t-Statistic Prob. YEAR 0.086958 0.003895 22.32804 0.0000C -169.4787 7.726922 -21.93353 0.0000R-squared 0.941459 Mean dependent var 3.046404Adjusted R-squared 0.939570 S.D. dependent var 0.866594S.E. of regression 0.213030 Akaike info criterion -0.196076Sum squared resid 1.406835 Schwarz criterion -0.105379Log likelihood 5.235258 F-statistic 498.5416Durbin-Watson stat 0.118575 Prob(F-statistic) 0.000000Plot-0.4-0.20.00.20.41234570 75 80 85 90 95 00Residual Actual FittedActual, Fitted and Residual Values from the Regressionof the Logarithm of General Fund Expenditures ($B) on YearNov. 2, 2000 ECON 240A-3 L. PhillipsMidterm5. (15 points) The monthly rate of return for the Gillette stock is regressed against the monthly rate of return for the Standard and Poor’s Composite Index, and the results are reported in the table below. A plot of actual, estimated and residual values follows.a. Interpret the economic meaning of the estimated coefficient on the Standard and Poor’s Composite Index.b. Is this estimated coefficient significantly different from zero, at the 5% level? Explain.c. Is this estimated coefficient significantly different from one at the 5% level? Explain.d. What is the economic significance of the test in part b? What is the economic significance of the test in part c?e. Interpret the economic meaning of the estimated coefficient of determination.f. What do you conclude from the combination of the information in R2 and the information in the plot of actual, fitted and residual values?TableDependent Variable: GILLETTEMethod: Least SquaresDependent Variable: GILLETTESample: 1993:01 1996:12Included observations: 48Variable Coefficient Std. Error t-Statistic Prob. C 0.011861 0.008030 1.477109 0.1465INDEX 0.776969 0.277141 2.803516 0.0074R-squared 0.145929 Mean dependent var 0.023018Adjusted R-squared 0.127362 S.D. dependent var 0.051722S.E. of regression 0.048316 Akaike info criterion -3.181347Sum squared resid 0.107383 Schwarz criterion -3.103380Log likelihood 78.35232 F-statistic 7.859702Durbin-Watson stat 2.058895 Prob(F-statistic) 0.007377Nov. 2, 2000 ECON 240A-4 L. PhillipsMidtermPlot-0.15-0.10-0.050.000.050.100.15-0.2-0.10.00.10.293:01 93:07 94:01 94:07 95:01 95:07 96:01 96:07Residual Actual FittedActual, Fitted, and Residual Values from the Regression of Monthly Rate of Return for Gillette On Monthly Rate of Returnfor Standard and Poor's Composite
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