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Tests2002PL2 - TC 310 Fall 2002 MODES OF REASONING First...

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TC 310 MODES OF REASONING D. Hamermesh Fall 2002 First Midterm, September 26, 2002 Answer the questions in a blue book. The points for each are equal to the suggested minutes. Use a hand calculator where you wish. You may have one side of a sheet of paper with formulas. The exams will be handed back in class next Tuesday, October 1. Please read Chapter 13 for Tuesday. 1. (12 minutes) Jane wants to meet someone new and is looking through the Austin Chronicle personal ads. She is picky about who she goes out with, and is particularly concerned about height. Her ideal date is someone who is within one inch of her height, which is 67’’ (i.e., she wants someone between 66 and 68 inches). Here are the heights of men advertising in the Chronicle . Height: 71 73 72 70 72 69 70 68 68 69 71 70 67 a. Calculate the mean and standard deviation for this sample of 13 men. Calculate the coefficient of variation. Calculate the median too. b. Draw a histogram of the information. Can you convey the information in a way that would be especially useful to Jane? Does the density function appear to be well approximated by the normal? 2. (12 minutes) a. Many of the most intriguing ads don’t provide a height. What are Jane’s chances of meeting an ideal date if she responds to an ad without a reported height? Use the mean and standard deviation above and assume the distribution is normal. b. What crucial assumption did you need to make about the heights of men who don’t report their heights compared with those who do? Is this assumption realistic? How does this influence your estimate of Jane’s probability of getting an ideal date? c. If Jane had information from an entire year on men’s heights (i.e. she had 1000 observations, not 13), would the estimates above change? Would having more observations be useful? Why or why not?
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3. (12 minutes) This year our TA ran in the Capitol 10K, an annual 10-kilometer (6.2138 mile) run through downtown Austin. Her time was 58 minutes. The average time of timed runners in the race was 60 minutes, with a standard deviation of 12. a. Assuming the distribution of finish times is distributed normally, what percentile was she in terms of her finish time? b. Her goal for next year is to finish in 52 minutes. If she meets the goal, what percentage of runners will beat her? What assumption are you making about the finish times next year, compared to the finish times this year? c. I would like to compare how fast people ran in the Capitol 10K with how fast they ran in the Turkey Trot, a 5-mile run on Thanksgiving Day. If people run at the same rate as they run the Capitol 10K, calculate what you expect will be the average and standard deviation of times in the Turkey Trot. d. Many runners do not time their race results, since obtaining a timing chip adds $1 to the entry fee. If we could obtain times on all runners in the Capitol 10K, how do you think the mean and standard deviations would differ compared to those for whom times were recorded? If the distribution of recorded times is normal, how would the
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