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mid1probs - Statistics 21 Problems from past midterms...

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Page 1 Statistics 21 Problems from past midterms: midterm 1 1. (5 points) The quotations below are taken from an article in the San Francisco Chronicle of May 31, 1989. The article begins: “In recent years, statistics has shown that drinking a little alcohol is good for your health.” (a) Has this been shown on the basis of controlled experiments? The article continues: Some studies even suggest that moderate drinkers live longer than people who don’t drink any alcohol. Researchers refer to this phenomenon as the U-shaped alcohol-mortal- ity curve. Non-drinkers and heavy drinkers are on opposite sides of the curve with the highest death rates. Moderate drinkers fall in the middle, with fewer early deaths from disease. A new study of 7,700 British men, however, suggests that there’s more to this curve than meets the eye.” The article goes on to describe how the investigators in the new study analyzed the non- drinking group. These were the men who, at the time of the study, said they were not drinking. As the investigators expected from the earlier studies, the non-drinkers, as a group, turned out to be not as healthy as the moderate drinkers. But the investigators went further. They found that a large number of the men in the non-drinking group had something in common. The investigators then removed the men with this common characteristic from the non-drinking group. They found that, overall, the remaining non-drinkers were just as healthy as the moderate drinkers. (b) As a group, were the removed men more, or less, healthy than the moderate drinkers? (c) What was the common characteristic? 2. (10 points) One number is missing from the data set below: x y 1 2 1 2 3 3 3 If possible, fill in the blank to make the correlation coefficient equal to 0. If it is not pos- sible, say why not.
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Page 2 3. (10 points) An instructor gives two quizzes to the ten people in her course. On the first quiz, five of the people were above average; but on the second quiz, these people all scored below average. The other five people moved in the opposite direction. They were all below average on the first quiz, and above average on the second one. (a) True or False and explain: This is an example of the regression effect. (b) The correlation coefficient between the scores on the two quizzes: must be zero. must be a positive number. must be a negative number. could be any of the above, depending on whether or not there are outliers in the data. Check (√) one option. Explain your choice. 4. (10 points) Here are the summary statistics for a large group of male students at a certain university. Height: Average = 70.0 inches, SD = 3.0 inches Weight: Average = 162 pounds, SD = 30 pounds correlation coefficient = 0.50 The scatter diagram is football shaped. About what percent of the men 74 inches tall weigh less than the average weight of the men 66 inches tall?
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