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Unformatted text preview: TC 310 D. Hamermesh MODES OF REASONING Fall 2006 First Midterm, September 28, 2006 Answer Key I. I. (15 minutes) Calculate the mean, standard deviation, median, interquartile range and coefficient of variation of the motor vehicle death rate for this group of states. Don’t worry about the age for license just yet. State Age for License Motor Vehicle Death Rate CA 18 1.7 FL 16 2.3 GA 21 1.9 IA 18 2.1 NY 17 1.9 OR 16 1.8 TX 16 2.0 VA 18 1.6 WI 18 1.8 mean 1.9 std dev 0.212 median 1.9 or a number like 1.87 1st quartile 1.8 or 1.725 3rd quartile 2 or 1.975 interquartile range 0.2 or 0.25 coefficient of variation 0.112 II. (71/2 minutes) 1. What would you expect the relationship to be between the two series shown above? Why? Is this correlation, or is causation implied? Explain. Although one cannot say for sure that there is a causal relationship between the motor vehicle death rate and age per se , it is reasonable to say that there is another variable correlated with age, say driving experience, which affects the likelihood of getting into a car accident. Hence, we expect age implicitly to cause differences in the motor vehicle death rate. 2. Draw a scatter plot of these points, and say what you think the correlation between the series is. Comment on the extent of the correlation between the two series. agedeath rate 1 1.2 1.4 1.6 1.8 2 2.2 2.4 13 15 17 19 21 23 age death rate agedeath rate As one would have expected, the scatter plot indicates a negative correlation between the two series, since a downward sloping line would fit best the plot. That is, the older you are, the less likely it is that you are going to be killed in a car accident. However, the points are somewhat dispersed around a fitted imagined line, indicating that the correlation is not too high. This is a football, indicating a weak negative correlation, and the correlation is 0.30. III. (15 minutes) Every March, 64 college basketball teams compete in a tournament for the National Championship. The table below shows the winloss ratios for the teams predicted to be invited. WinLoss Ratio Number of Teams .550  .599 2 .600  .649 4 .650  .699 18 .700  .749 9 .750  .799 14 .800  .849 11 .850  .899 2 .900  .949 1 .950  .999 3 1. Draw a histogram using these data. Number of teams 5 10 15 20 winloss ratio n u m be r .550  .599 .600  .649 .650  .699 .700  .749 .750  .799 .800  .849 .850  .899 .900  .949 .950  .999 2. Is the normal distribution a good approximation to the data? The normal distribution does not seem to be a good approximation, or only a very rough one. The distribution gets thinner at its tails, but it does not peak at its “middle”. It is not really symmetric, either....
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 Fall '07
 HAMERMESH
 Normal Distribution, Standard Error, Null hypothesis, vehicle death rate, motor vehicle death

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