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CHAPTER 11 SOLUTIONS AND MINI-PROJECT NOTES CHAPTER 11 RELATIONSHIPS CAN BE DECEIVING EXERCISE SOLUTIONS 11.1 Both firewood sales and cough drop sales are likely to increase during the cold season. No, it does not imply that fires cause coughs! 11.2 No, you wouldn't necessarily conclude that walking causes lower weight. People who prefer to exercise (walk) may also be people who keep their weight under control, eat less fat, and so on. 11.3 Reason 1 could be possible but isn't likely, that milk-drinking alone is responsible for low risk of stroke. Reason 2 is not likely, since it would say that a low risk of stroke causes people to drink milk, and vice versa. People don't usually even know whether or not they are at risk for strokes. Reason 3 could be possible, that milk-drinking is one of many factors that reduces the risk of a stroke. Reason 4 is quite likely, that confounding variables exist. One example is general good diet and good health, which leads to reduced stroke risk. Reason 5 is likely, that both reduced stroke risk and increased milk-consumption result from a common cause, such as interest in taking care of one's health. Related to reasons 4 and 5, note that the article made a point of saying that the same individuals who consumed the most milk were also "leanest and most physically active." Reason 6 , that both variables are changing over time, is not relevant, unless the study did not adjust for age and the men drank less milk as they aged, which would also increase stroke risk. Reason 7 , that the association is just a coincidence, is possible. Any single study could find a relationship just by chance. 11.4 a. See Figure 11.1 below. b. If X-rays were deleted, the correlation would decrease (to 0.13 in case you are interested), because outliers that fall in line with the rest of the data tend to increase correlation. If pesticides were deleted (but not X-rays) correlation would increase (to 0.68), because outliers that do not fit the pattern of the rest of the data tend to decrease correlation. c. That would decrease the correlation because it would be an extreme outlier, not in line with the data. It also makes sense that it should decrease the correlation because it is an example of a case in which the students and experts are not in agreement at all, and thus weakens the relationship. Figure 11.1 for Exercise 11.4a 11.5 Winning time in an Olympic running event and the cost of running shoes are likely to be negatively Page 1 of 4
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CHAPTER 11 SOLUTIONS AND MINI-PROJECT NOTES correlated because prices go up and winning times go down over time. 11.6 They are designed to rule out Reason 4, "confounding variables may exist." 11.7 a. See Figure 11.2 below. The lines are almost parallel, and the regression line falls entirely below the actual = ideal line. This indicates that when averaged over males and females, the data imply that people's ideal and actual weight are very similar, with ideal weight always being slightly less than actual weight. b.
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This note was uploaded on 10/15/2011 for the course STAT 100 at Penn State.

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