Nov. 2, 2004 ECON 240A-1 L. PhillipsMidterm1. (15) The box plot for running times from a random sample of Boston Marathon runners is shown below. Table 1-1 lists the data sorted in descending order.a. Label the median on the plot with its numerical value.b. Label the first and third quartiles on the plot with their numerical values.c. The numerical value for the second quartile is also the numerical value forthe ____________ .d. Label the ends of the upper whisker and the lower whisker with their numerical values.e. How many outliers are there? What does it take to be an outlier? Table 1-1. Random Sample of Running Times, Boston Marathon219.96 172.2 150.51 140.1201.79 171.46 147.78192.84 171.33 146.67191.42 170.43 146.59185.41 169.49 145.91183.97 165.63 145.11178.38 165.08 144.69177.64 165.06 144.41176.98 164.87 143.96176.6 164.17 143.76176.29 160.88 143.44175.58 158.75 142.33175.21 158.53 141.97175.18 158.39 141.83174.09 156.9 141.18173.9 153.34 141.06173.24 152.07 140.95173.18 152.03 140.57Nov. 2, 2004 ECON 240A-2 L. PhillipsMidterm2. (15) A random sample of heart attack victims can be classified as high income, 30%, medium income, 49%, and low income, 21%, respectively. These heart attack victims were classified as either survivors or deceased. Of those deceased, 7% were high income, 9% were medium income, and 12% were low income.a. What is the joint probability of a sample member being low income and a heart attack survivor? _________________b. What is the conditional probability of a member being a survivor given that they are low income? __________________c. Is this conditional probability (part b) higher or lower than the probability of a member being a survivor? __________________d. What is the conditional probability of a member being a survivor given that the member is high income? __________________e. Does survival of a heart attack appear to be independent of income? _____3. (15) The owner of a low-tech parking lot suspects her employee may be embezzling or skimming. Based on the dollar receipts the employee provided, the average time parked would be 3.5 hours. For the same period as the receipts turned in, the owner had the lot under surveillance and the following information on parking times was obtained. The histogram of parking times is shown as Fig.3-1. The summary statistics for parking times is included as Table3-1.a. What is the recommended range for the number of bins for a histogram fora data set this size? ___________b. At a 1% level of significance, do you think the employee is embezzling or not?_____________c. What is the critical value in the distribution determining the probability of the type I error?_____________d. What distribution did you use in your answer to parts b and c? _________.Why? ___________.e. If the histogram of parking times is not normal, does it affect your answer?__________________________________Nov. 2, 2004 ECON 240A-3 L. PhillipsMidtermFigure 3-1: Histogram of Parking Times in Hours0501001502002.252.52.7533.253.53.7544.254.54.75BinFrequencyTable 3-1. Summary Statistics, Parking Times in HoursMean 3.61Standard Error 0.015934Median 3.6Mode 3.7Standard Deviation 0.4Sample Variance 0.16Kurtosis 0.329372Skewness -0.07103Range 2.7Minimum 2Maximum 4.7Sum 2271.7Count 6294. (15) Describe in words why you could make errors ina. estimating the population mean from a sample of random numbers generated from the normal distribution with mean zero and variance one.b. estimating the proportion of voters that will vote for Senator Boxer today, based on a Field Poll taken three weeks ago.c. estimating the true average monthly rate of return on the UC Stock Index Fund from five years of monthly data used to calculate the sample mean ofthe monthly rate of return of this index.Nov. 2, 2004 ECON 240A-4 L. PhillipsMidterm5. (15) Employment in California (in millions of persons) is plotted against Real California Personal Income (in millions of 2000 $), as illustrated in Figure 5-1. There appears to be “diminishing returns” so to speak, i.e. the slope of the data points appears to decrease as the ratio of employment to real income decreases. Note that a linear relationship does not fit the beginning or ending data points well. Figure 5-1: CA Employm ent Vs Real CA Personal Incom e(2000 $), 1971-200320031971y = 1E-05x + 4.1866R2 = 0.96570246810121416180 200,000 400,000 600,000 800,000 1,000,000 1,200,000R eal C A P erso nal Income, MillionsThe ratio of employees per real dollar(2000) of personal income was calculated and plotted against time, where time equals zero in 1971 and time equals 32 in 2003. Thisratio of employee per 2000 dollar equals 21 per million dollars in 1971 and 14 per milliondollars in 2003. This trend plot is shown in Figure 5-2. The regression results are shown in Table5-1. A plot of the residuals from this trend regression is shown in Fig. 5-3.a. Is there a statistically significant trend in the ratio? ____________b. How do you know? _____________________________________c. What is the estimated value of the ration in 1971? ____________d. Does the 95% confidence interval on the estimated intercept include the actualvalue of the ratio in 1971? _____________e. . Does this regression obviously violate any of the assumptions of ordinary least squares (OLS)? ____________________Nov. 2, 2004 ECON 240A-5 L. PhillipsMidtermTable 5-1: Regression of Employee Per 2000 Dollar of Personal Income Vs. TimeRegression StatisticsMultiple R 0.9767937R Square 0.954126Adjusted R Square 0.9526462Standard Error 4.165E-07Observations 33ANOVA df SS MS FSignificanceFRegression 1 1.11865E-10 1.12E-10 644.76372.60982E-22Residual 31 5.37843E-12 1.73E-13Total 32 1.17243E-10 CoefficientsStandardError t Stat P-value Lower 95%Upper95%Intercept 2.106E-05 1.41782E-07 148.5202 8.6E-462.07684E-052.1347E-05X Variable 1 -1.934E-07 7.61493E-09 -25.3922 2.61E-22 -2.0889E-07-1.778E-07Nov. 2, 2004 ECON 240A-6 L. PhillipsMidterm-0.0000010-0.00000050.00000000.00000050.00000100.0000140.0000160.0000180.0000200.00002275 80 85 90 95 00Residual Actual FittedFigure 5-3: A plot of the Actual Ratio, the Fitted Ratio, and the ResidualsNov. 2, 2004 ECON 240A-7 L. PhillipsMidtermFrom the graph above, it appears a linear relationship might fit the 70’s pretty well, and a different linear relationship, with a bigger intercept and a smaller slope might fit the eighties pretty well, and yet a different linear relationship, with the largest interceptand the smallest