Stat 1350 - Elementary Statistics Graded Homework Assignment 3 Chapters 5, 6 and 7 5.2 Exhaust is bad for your heart. A CNET News article reported that the artery walls of people living within 100 meters of a highway thicken more than twice as fast as the average person's. Researchers used ultrasound to measure the carotid artery wall thickness of 1483 people living near freeways in the Los Angeles area. The artery wall thickness among those living within 100 meters of a highway increased by 5.5 micrometers (roughly 1/20th the thickness of a human hair) each year during the three-year study, which is more than twice the progression observed in participants who did not live within this distance of a highway. (a) What are the explanatory and response variables? (b) Who are the subjects? (c) Explain carefully why this study is not an experiment. (d) Explain why confounding prevents us from concluding that living near a highway is bad for your heart because it causes increased thickness in the carotid artery wall. 5.4 Weight-loss surgery and longer life. An article in the Washington Post reported that, according to two large studies, obese people are significantly less likely to die prematurely if they undergo stomach surgery to lose weight. But people choose whether to have stomach surgery. Explain why this fact makes any conclusion about cause and effect untrustworthy. Use the language of lurking variables and confounding in your explanation, and draw a picture like Figure 5.1 (below) to illustrate it. 5.8 Neighborhood's effect on grades. To study the effect of neighborhood on academic performance, one thousand families were given federal housing vouchers to move out of their lowincome neighborhoods. No improvement in the academic performance of the children in the families was found one year after the move. Explain clearly why the lack of improvement in academic performance after one year does not necessarily mean that neighborhood does not affect academic performance. In particular, identify some lurking variables whose effect on academic performance may be confounded with the effect of neighborhood. Use a picture like Figure 5.1 on previous page to illustrate your explanation. 5.6 Aspirin and heart attacks. Can aspirin help prevent heart attacks? The Physicians' Health Study, a large medical experiment involving 22,000 male physicians, attempted to answer this question. One group of about 11,000 physicians took an aspirin every second day, while the rest took a placebo. After several years the study found that subjects in the aspirin group had significantly fewer heart attacks than subjects in the placebo group. (a) Identify the experimental subjects, the explanatory variable and the values it can take, and the response variable. (b) Use a diagram to outline the design of the Physicians' Health Study. (When you outline the design of an experiment, be sure to indicate the size of the treatment groups and the response variable. The diagrams in Figure 5.2 and Figure 5.3 given below are models.) Practice this! You will be asked to do this on the test!!! (c) What do you think the term \"significantly\" means in \"significantly fewer heart attacks\"? Figure 5.2 5.14 Table saw blades. A manufacturer of table saw blades is interested in determining whether a narrower blade will cause less burning of wood when cutting very hard woods, such as maple. To answer this question, engineers obtain 20 similar one-inch-thick hard maple boards. Half are sawed using the new, narrow-style blade, and the other half are sawed using the standard-width blade. All cuts are done at the same feed rate (the rate at which the board is pushed against the blade to make the cut). The engineers then measure the amount of burning (rated on a scale of 1 to 10, with 10 being the worst) on each board. (a) The individuals studied in this experiment are not people. What are they? (b) What is the explanatory variable, and what values does it take? (c) What is the response variable, and what values does it take? (d) What are the treatments? 5.11 Do antioxidants prevent cancer? People who eat lots of fruits and vegetables have lower rates of colon cancer than those who eat little of these foods. Fruits and vegetables are rich in \"antioxidants\" such as vitamins A, C, and E. Will taking antioxidants help prevent colon cancer? A clinical trial studied this question with 864 people who were at risk for colon cancer. The subjects were divided into four groups: daily beta-carotene, daily vitamins C and E, all three vitamins every day, and daily placebo. After four years, the researchers were surprised to find no significant difference in colon cancer among the groups. (a) What are the explanatory and response variables in this experiment? (b) Outline the design of the experiment. (The diagrams in Figure 5.2 and Figure 5.3 are models.) (c) Assign labels to the 864 subjects and use Table A, starting at line 118, to choose the first 5 subjects for the beta-carotene group. (d) What does \"no significant difference\" mean in describing the outcome of the study? (e) Suggest some lurking variables that could explain why people who eat lots of fruits and vegetables have lower rates of colon cancer. The results of the experiment suggest that these variables, rather than the antioxidants, may be responsible for the observed benefits of fruits and vegetables. Figure 5.3 5.18 Statistical significance. A randomized comparative experiment examines whether the usual care of patients with chronic heart failure plus aerobic exercise training improves health status compared with the usual care alone. The researchers conclude that usual care plus exercise training confers modest but statistically significant improvements in self-reported health status compared with usual care without training. Explain what \"statistically significant\" means in the context of this experiment, as if you were speaking to a patient who knows no statistics. 6.4 Do antidepressants help? A researcher studied the effect of an antidepressant on depression. He randomly assigned subjects with moderate levels of depression to two groups. One group received the antidepressant and the other a placebo. Subjects were blinded with respect to the