midterm 2008 key - Nov 4 2008 Answer All Five Questions...

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Nov. 4, 2008 ECON 240A- 1 L. Phillips Midterm Answer All Five Questions. 1. (15 min.) This is the o-ring failure data for launch temperature from the JMP data file. Distributions Temperature 50 55 60 65 70 75 80 85 H Quantiles 100.0% maximum 81.000 99.5% 81.000 97.5% 81.000 90.0% 78.600 75.0% quartile 75.000 50.0% median 70.000 25.0% quartile 67.000 10.0% 57.400 2.5% 53.000 0.5% 53.000 0.0% minimum 53.000 Moments Mean 69.565217 Std Dev 7.0570795 Std Err Mean 1.4715028 upper 95% Mean 72.616927 lower 95% Mean 66.513507 N 23 a. What kind of graph is on the left, above? Histogram b. In the diagram to the right, above, draw an arrow to and label the 25 th percentile. c. In the diagram to the right, above, draw an arrow to and label the median. d. Is the median above or below the mean? Above e. In the diagram to the right, above, draw an arrow to and label the outlier. 25 th Percentile Median Outlier
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Nov. 4, 2008 ECON 240A- 2 L. Phillips Midterm 2. (15 Min.) This is the weight data from the JMP Student file that we examined in HSSB. Distributions weight 50 70 90 110 130 150 170 190 Quantiles 100.0% maximum 196.00 99.5% 188.35 97.5% 145.30 90.0% 121.00 75.0% quartile 112.00 50.0% median 100.00 25.0% quartile 85.00 10.0% 78.40 2.5% 69.00 0.5% 53.21 0.0% minimum 51.00 Moments Mean 100.91416 Std Dev 19.184706 Std Err Mean 1.2568319 upper 95% Mean 103.39043 lower 95% Mean 98.4379 N 233 a. What is the sample mean? 100.91 b. What is the sample standard deviation? 19.185 c. The diamond in the box diagram illustrates a 95% confidence interval for the population mean inferred from the sample. Calculate this 95% confidence interval. Show your work . Use Student’s t-distribution. For 232 degrees of freedom, use 200 dof in Table in back of the book. The critical values are =/- 1.97. See above. Prob(-1.97≤ (xˉ - µ)/(s/√n) ≤ 1.97) = 0.95 Prob(-1.97≤ (100.91 - µ)/(19.185/√233) ≤ 1.97) = 0.95 Prob(-1.97≤ (100.91 - µ)/(19.185/15.264) ≤ 1.97) = 0.95 Prob(-1.97≤ (100.91 - µ)/1.257 ≤ 1.97) = 0.95 Prob(-2.48≤ (100.91 - µ) ≤ 2.48) = 0.95 Prob(2.48≥ ( µ - 100.91) ≥ -2.48) = 0.95 Prob(100.91 + 2.48≥ µ ≤ 100.91 -2.48) = 0.95 Prob(103.39 µ ≤ 98.43) = 0.95
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Nov. 4, 2008 ECON 240A- 3 L. Phillips Midterm 3. (15 Min.) Two weeks before the election on this November 4 th , three western states were still in play, Nevada with five electoral votes, New Mexico with five electoral votes, and Colorado with nine electoral votes. Assume that for states in play the probability that Obama or McCain winning the state is 50%. Also assume winning one of these three
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