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mid1probs - Statistics 2 Problems from past midterms...

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Page 1 Statistics 2 Problems from past midterms: midterm 1 1. (10 points) The men enrolled in a large physiology course had an average weight of 160 pounds and an SD of 25 pounds. Their weights followed the normal curve closely. (a) About what percent of the men weighed between 180 and 200 pounds? (b) Out of just those men—that is, the ones who weighed between 180 and 200 pounds— about what percent weighed between 180 and 190 pounds? 2. (10 points) A distribution table for family income is shown below. The class intervals include the left end-point but not the right. (The table is a much simplified version of the 1991 income distribution of US families receiving a social security cheque.) Income Percentage (in thousands of dollars) (of families) 0 10 20 10 30 45 30 50 20 50 – 100 15 (a) Plot the histogram. Mark the horizontal and vertical scales carefully. Label the axes. (b) True or False, and explain: ‘The median is $20,000.” 3. (5 points) There are 300 students in a large physical education class. The instructor gives everyone in the class a reaction time test and a physical dexterity test. The dex- terity test is scored out of 10 points. The averages for the class are as follows: average reaction time: 382 milliseconds average dexterity score: 7.4 points The instructor compares two methods for predicting the dexterity score of someone in the class: Method 1: Ignore any information about the person. Just use the average 7.4 points as the prediction. Method 2: Take the reaction time of the person, and use the regression method to predict his or her dexterity test score. The instructor works out the r.m.s. error for each method and finds that the two r.m.s. errors are about equal to one another. The correlation coefficient between reaction time and dexterity score (for the students in the course) must be around: –0.1 –0.5 –0.9 can’t tell without more information Please circle your choice and then explain it.
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Page 2 4. (5 points) The height and weight of a group of five men are shown in the table below: Person Height Weight A 67 158 B 69 162 C 70 160 D 71 154 E 73 166 Height is measured in inches and weight in pounds. One of these five men is going to be picked somehow or other and a statistician must estimate the weight of that man–but without being told the height. The statistician knows the numbers in the table.
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