Tomatoes Describe a strategy to randomly split the 24

Steroids The 1990s and early 2000s could be considered the steroids era in Major League Baseball, as many players have admitted to using the drug to increase performance on the field. If a sports writer wanted to compare home run totals from the steroids era to an earlier decade, say the 1960s, explain why this would be an observational study. Could the writer conclude that it was the steroids that caused the increase in home runs? Why or why not?

Problem 2E E-commerce A business student conjectures that the Internet caused companies to become more profitable, since many transactions previously handled “face-to-face” could now be completed online. The student compares earnings from a sample of companies from the 1980s to a sample from the 2000s. Explain why this is an observational study. If indeed profitability increased, can she conclude the Internet was the cause? Why or why not?

What design? Analyze the design of each research example reported. Is it a sample survey, an observational study, or an experiment? If a sample, what are the population, the parameter of interest, and the sampling procedure? If an observational study, was it retrospective or prospective? If an experiment, describe the factors, treatments, randomization, response variable, and any blocking, matching, or blinding that may be present. In each, what kind of conclusions can be reached? Researchers identified 242 children in the Cleveland area who had been born prematurely (at about 29 weeks). They examined these children at age 8 and again at age 20, comparing them to another group of 233 children not born prematurely. Their report, published in the New England Journal of Medicine, said the “preemies” engaged in significantly less risky behavior than the others. Differences showed up in the use of alcohol and marijuana, conviction of crimes, and teenage pregnancy.

Problem 2RE What design? Analyze the design of each research example reported. Is it a sample survey, an observational study, or an experiment? If a sample, what are the population, the parameter of interest, and the sampling procedure? If an observational study, was it retrospective or prospective? If an experiment, describe the factors, treatments, randomization, response variable, and any blocking, matching, or blinding that may be present. In each, what kind of conclusions can be reached? The journal Circulation reported that among 1900 people who had heart attacks, those who drank an average of 19 cups of tea a week were 44% more likely than nondrinkers to survive at least 3 years after the attack.

Problem 3E Tips A pizza delivery driver, always trying to increase tips, runs an experiment on his next 40 deliveries. He flips a coin to decide whether or not to call a customer from his mobile phone when he is five minutes away, hoping this slight bump in customer service will lead to a slight bump in tips. After 40 deliveries, he will compare the average tip percentage between the customers he called and those he did not. What are the experimental units and how did he randomize treatments?

Problem 3RE Homecoming. A college Statistics class conducted a survey concerning community attitudes about the college’s large homecoming celebration. That survey drew its sample in the following manner: Telephone numbers were generated at random by selecting one of the local telephone exchanges (first three digits) at random and then generating a random four-digit number to follow the exchange. If a person answered the phone and the call was to a residence, then that person was taken to be the subject for interview. (Undergraduate students and those under voting age were excluded, as was anyone who could not speak English.) Calls were placed until a sample of 200 eligible respondents had been reached. a) Did every telephone number that could occur in that community have an equal chance of being generated? ________________ b) Did this method of generating telephone numbers result in a simple random sample (SRS) of local residences? Explain. ________________ c) Did this method generate an SRS of local voters? Explain. ________________ d) Is this method unbiased in generating samples of households? Explain.

Problem 4E Tomatoes You want to compare the tastiness and juiciness of tomatoes grown with three amounts of a new fertilizer: none, half the recommended amount, and the full recommended amount. You allocate 6 tomato plants to receive each amount of fertilizer, assigning them at random. What are the experimental units? What is the response variable?

Problem 4RE Youthful appearance. Readers’ Digest (April 2002, p. 152) reported results of several surveys that asked graduate students to examine photographs of men and women and try to guess their ages. Researchers compared these guesses with the number of times the people in the pictures reported having sexual intercourse. It turned out that those who had been more sexually active were judged as looking younger, and that the difference was described as “statistically significant.” Psychologist David Weeks, who compiled the research, speculated that lovemaking boosts hormones that “reduce fatty tissue and increase lean muscle, giving a more youthful appearance.” a) What does “statistically significant” mean in this context? ________________ b) Explain in statistical terms why you might be skeptical about Dr. Weeks’s conclusion. Propose an alternative explanation for these results.

Problem 5E Tips II For the experiment described in Exercise 3, list the factor, the levels, and the response variable. Exercise 3: Tips A pizza delivery driver, always trying to increase tips, runs an experiment on his next 40 deliveries. He flips a coin to decide whether or not to call a customer from his mobile phone when he is five minutes away, hoping this slight bump in customer service will lead to a slight bump in tips. After 40 deliveries, he will compare the average tip percentage between the customers he called and those he did not. What are the experimental units and how did he randomize treatments?

What design? Analyze the design of each research example reported. Is it a sample survey, an observational study, or an experiment? If a sample, what are the population, the parameter of interest, and the sampling procedure? If an observational study, was it retrospective or prospective? If an experiment, describe the factors, treatments, randomization, response variable, and any blocking, matching, or blinding that may be present. In each, what kind of conclusions can be reached? Data were collected over a decade from 1021 men and women with a recent history of precancerous colon polyps. Participants were randomly assigned to receive folic acid (a B vitamin) or a placebo, and the study concluded that those receiving the folic acid may actually increase their risk of developing additional precancerous growths. Previous studies suggested that taking folic acid may help to prevent colorectal cancer. (Source: JAMA 2007, 297)

Problem 6E Tomatoes II For the experiment described in Exercise 4, name the factor and its levels. How might the response be measured? Exercise 4: Tomatoes You want to compare the tastiness and juiciness of tomatoes grown with three amounts of a new fertilizer: none, half the recommended amount, and the full recommended amount. You allocate 6 tomato plants to receive each amount of fertilizer, assigning them at random. What are the experimental units? What is the response variable?

What design? Analyze the design of each research example reported. Is it a sample survey, an observational study, or an experiment? If a sample, what are the population, the parameter of interest, and the sampling procedure? If an observational study, was it retrospective or prospective? If an experiment, describe the factors, treatments, randomization, response variable, and any blocking, matching, or blinding that may be present. In each, what kind of conclusions can be reached? In the journal Science, a research team reported that plants in southern England are flowering earlier in the spring. Records of the first flowering dates for 385 species over a period of 47 years indicate that flowering has advanced an average of 15 days per decade, an indication of climate warming, according to the authors.

Problem 7RE Smoking and Alzheimer’s. Medical studies indicate that smokers are less likely to develop Alzheimer’s disease than people who never smoked. a) Does this prove that smoking may offer some protection against Alzheimer’s? Explain. ________________ b) Offer an alternative explanation for this association. ________________ c) How would you conduct a study to investigate this?

Tips again For the experiment of Exercise 3, name some variables the driver did or should have controlled. Was the experiment randomized and replicated?

Problem 8E Tomatoes again For the experiment of Exercise 4, discuss variables that could be controlled or that could not be controlled. Is the experiment randomized and replicated? Exercise 4: Tomatoes You want to compare the tastiness and juiciness of tomatoes grown with three amounts of a new fertilizer: none, half the recommended amount, and the full recommended amount. You allocate 6 tomato plants to receive each amount of fertilizer, assigning them at random. What are the experimental units? What is the response variable?

More tips Is the experiment of Exercise 3 blinded? Can it be double-blinded? Explain.

What design? Analyze the design of each research example reported. Is it a sample survey, an observational study, or an experiment? If a sample, what are the population, the parameter of interest, and the sampling procedure? If an observational study, was it retrospective or prospective? If an experiment, describe the factors, treatments, randomization, response variable, and any blocking, matching, or blinding that may be present. In each, what kind of conclusions can be reached? Does keeping a child’s lunch in an insulated bag, even with ice packs, protect the food from warming to temperatures where germs can proliferate? Researchers used an electric temperature gun on 235 lunches at preschools 90 minutes before they were to be eaten. Of the lunches with ice packs, over 90% of them were at unsafe temperatures. The study was of particular interest because preschoolers develop up to four times as many foodborne infections as do adults. (Source: Science News, August 9, 2011)

Problem 10E More tomatoes If the tomato taster doesn’t know how the tomatoes have been treated, is the experiment single or double-blind? How might the blinding be improved further?

What design? Analyze the design of each research example reported. Is it a sample survey, an observational study, or an experiment? If a sample, what are the population, the parameter of interest, and the sampling procedure? If an observational study, was it retrospective or prospective? If an experiment, describe the factors, treatments, randomization, response variable, and any blocking, matching, or blinding that may be present. In each, what kind of conclusions can be reached? Some doctors have expressed concern that men who have vasectomies seemed more likely to develop prostate cancer. Medical researchers used a national cancer registry to identify 923 men who had had prostate cancer and 1224 men of similar ages who had not. Roughly one quarter of the men in each group had undergone a vasectomy, many more than 25 years before the study. The study’s authors concluded that there is strong evidence that having the operation presents no long-term risk for developing prostate cancer. (Source: Science News, July 20, 2002)

Problem 11E Block that tip The driver of Exercise 3 wants to know about tipping in general. So he recruits several other drivers to participate in the experiment. Each driver randomly decides whether to phone customers before delivery and records the tip percentage. Is this experiment blocked? Is that a good idea? Exercise 3: Tips A pizza delivery driver, always trying to increase tips, runs an experiment on his next 40 deliveries. He flips a coin to decide whether or not to call a customer from his mobile phone when he is five minutes away, hoping this slight bump in customer service will lead to a slight bump in tips. After 40 deliveries, he will compare the average tip percentage between the customers he called and those he did not. What are the experimental units and how did he randomize treatments?

Problem 11RE What design? Analyze the design of each research example reported. Is it a sample survey, an observational study, or an experiment? If a sample, what are the population, the parameter of interest, and the sampling procedure? If an observational study, was it retrospective or prospective? If an experiment, describe the factors, treatments, randomization, response variable, and any blocking, matching, or blinding that may be present. In each, what kind of conclusions can be reached? Widely used antidepressants may reduce ominous brain plaques associated with Alzheimer’s disease. In the study, mice genetically engineered to have large amounts of brain plaque were given a class of antidepressants that boost serotonin in the brain. After a single dose, the plaque levels dropped, and after four months, the mice had about half the brain plaques as the mice that didn’t take the drug. (Source: Proceedings of the National Academy of Sciences, August 22, 2011)

Problem 12E Blocking tomatoes To obtain enough plants for the tomato experiment of Exercise 4, experimenters have to purchase plants from two different garden centers. They then randomly assign the plants from each garden center to all three fertilizer treatments. Is the experiment blocked? Is that a good idea? Exercise 4: Tomatoes You want to compare the tastiness and juiciness of tomatoes grown with three amounts of a new fertilizer: none, half the recommended amount, and the full recommended amount. You allocate 6 tomato plants to receive each amount of fertilizer, assigning them at random. What are the experimental units? What is the response variable?

Problem 12RE Pubs. In England, a Leeds University researcher said that the local watering hole’s welcoming atmosphere helps men get rid of the stresses of modern life and is vital for their psychological well-being. Author of the report, Dr. Colin Gill, said rather than complain, women should encourage men to “pop out for a swift half.” “Pub-time allows men to bond with friends and colleagues,” he said. “Men need break-out time as much as women and are mentally healthier for it.” Gill added that men might feel unfulfilled or empty if they had not been to the pub for a week. The report, commissioned by alcoholfree beer brand Kaliber, surveyed 900 men on their reasons for going to the pub. More than 40% said they went for the conversation, with relaxation and a friendly atmosphere being the other most common reasons. Only 1 in 10 listed alcohol as the overriding reason. Let’s examine this news story from a statistical perspective. a) What are the W’s: Who, What, When, Where, Why, How? ________________ b) What population does the researcher think the study applies to? ________________ c) What is the most important thing about the selection process that the article does not tell us? ________________ d) How do you think the 900 respondents were selected? (Name a method of drawing a sample that is likely to have been used.) ________________ e) Do you think the report that only 10% of respondents listed alcohol as an important reason for going to the pub might be a biased result? Why?

Problem 13E Confounded tips For the experiment of Exercise 3, name some confounding variables that might influence the experiment’s results? Exercise 3: Tips A pizza delivery driver, always trying to increase tips, runs an experiment on his next 40 deliveries. He flips a coin to decide whether or not to call a customer from his mobile phone when he is five minutes away, hoping this slight bump in customer service will lead to a slight bump in tips. After 40 deliveries, he will compare the average tip percentage between the customers he called and those he did not. What are the experimental units and how did he randomize treatments?

What design? Analyze the design of each research example reported. Is it a sample survey, an observational study, or an experiment? If a sample, what are the population, the parameter of interest, and the sampling procedure? If an observational study, was it retrospective or prospective? If an experiment, describe the factors, treatments, randomization, response variable, and any blocking, matching, or blinding that may be present. In each, what kind of conclusions can be reached? Tests of gene therapy on laboratory rats have raised hopes of stopping the degeneration of tissue that characterizes chronic heart failure. Researchers at the University of California, San Diego, used hamsters with cardiac disease, randomly assigning 30 to receive the gene therapy and leaving the other 28 untreated. Five weeks after treatment the gene therapy group’s heart muscles stabilized, while those of the untreated hamsters continued to weaken. (Source: Science News, July 27, 2002)

Problem 14E Tomatoes finis What factors might confound the results of the experiment in Exercise 4? Exercise 4: Tomatoes You want to compare the tastiness and juiciness of tomatoes grown with three amounts of a new fertilizer: none, half the recommended amount, and the full recommended amount. You allocate 6 tomato plants to receive each amount of fertilizer, assigning them at random. What are the experimental units? What is the response variable?

Problem 14RE What design? Analyze the design of each research example reported. Is it a sample survey, an observational study, or an experiment? If a sample, what are the population, the parameter of interest, and the sampling procedure? If an observational study, was it retrospective or prospective? If an experiment, describe the factors, treatments, randomization, response variable, and any blocking, matching, or blinding that may be present. In each, what kind of conclusions can be reached? People aged 50 to 71 were initially contacted in the mid-1990s to participate in a study about smoking and bladder cancer. Data were collected from more than 280,000 men and 186,000 women from eight states who answered questions about their health, smoking history, alcohol intake, diet, physical activity, and other lifestyle factors. When the study ended in 2006, about half the bladder cancer cases in adults age 50 and older were traceable to smoking. (Source: Journal of the American Medical Association, August 17, 2011)

Problem 15E Standardized test scores For his Statistics class experiment, researcher J. Gilbert decided to study how parents’ income affects children’s performance on standardized tests like the SAT. He proposed to collect information from a random sample of test takers and examine the relationship between parental income and SAT score. a) Is this an experiment? If not, what kind of study is it? ________________ b) If there is relationship between parental income and SAT score, why can’t we conclude that differences in score are caused by differences in parental income?

What design? Analyze the design of each research example reported. Is it a sample survey, an observational study, or an experiment? If a sample, what are the population, the parameter of interest, and the sampling procedure? If an observational study, was it retrospective or prospective? If an experiment, describe the factors, treatments, randomization, response variable, and any blocking, matching, or blinding that may be present. In each, what kind of conclusions can be reached? An orange-juice processing plant will accept a shipment of fruit only after several hundred oranges selected from various locations within the truck are carefully inspected. If too many show signs of unsuitability for juice (bruised, rotten, unripe, etc.), the whole truckload is rejected.

Problem 16RE Bias? Political analyst Michael Barone has written that “conservatives are more likely than others to refuse to respond to polls, particularly those polls taken by media outlets that conservatives consider biased” (Source: The Weekly Standard, March 10, 1997). The Pew Research Foundation tested this assertion by asking the same questions in a national survey run by standard methods and in a more rigorous survey that was a true SRS with careful follow-up to encourage participation. The response rate in the “standard survey” was 42%. The response rate in the “rigorous survey” was 71%. a) What kind of bias does Barone claim may exist in polls? ________________ b) What is the population for these surveys? ________________ c) On the question of political position, the Pew researchers report the following table: Standard Survey Rigorous Survey Conservative 37% 35% Moderate 40% 41% Liberal 19% 20% What makes you think these results are incomplete? ________________ d) The Pew researchers report that differences between opinions expressed on the two surveys were not statistically significant. Explain what “not statistically significant” means in this context.

Heart attacks and height Researchers who examined health records of thousands of males found that men who died of myocardial infarction (heart attack) tended to be shorter than men who did not. a) Is this an experiment? If not, what kind of study is it? b) Is it correct to conclude that shorter men are at higher risk of dying from a heart attack? Explain.

Problem 18RE What design? Analyze the design of each research example reported. Is it a sample survey, an observational study, or an experiment? If a sample, what are the population, the parameter of interest, and the sampling procedure? If an observational study, was it retrospective or prospective? If an experiment, describe the factors, treatments, randomization, response variable, and any blocking, matching, or blinding that may be present. In each, what kind of conclusions can be reached? Does the use of computer software in Introductory Statistics classes lead to better understanding of the concepts? A professor teaching two sections of Statistics decides to investigate. She teaches both sections using the same lectures and assignments, but gives one class statistics software to help them with their homework. The classes take the same final exam, and graders do not know which students used computers during the semester. The professor is also concerned that students who have had calculus may perform differently from those who have not, so she plans to compare software vs. no-software scores separately for these two groups of students.

Problem 17RE What design? Analyze the design of each research example reported. Is it a sample survey, an observational study, or an experiment? If a sample, what are the population, the parameter of interest, and the sampling procedure? If an observational study, was it retrospective or prospective? If an experiment, describe the factors, treatments, randomization, response variable, and any blocking, matching, or blinding that may be present. In each, what kind of conclusions can be reached? Older Americans with a college education are significantly more likely to be emotionally well-off than are people in this age group with less education. Among those aged 65 and older, 35% scored 90 or above on the Emotional Health Index, but for those with a college degree, the percentage rose to 43% (post-graduate degree, 46%). The results are based on phone interviews conducted between January 2010 and July 2011. (Source: gallup.com, August 19, 2011)

Problem 18E Super Bowl commercials When spending large amounts to purchase advertising time, companies want to know what audience they’ll reach. In January 2011, a poll asked 1008 American adults whether they planned to watch the upcoming Super Bowl. Men and women were asked separately whether they were looking forward more to the football game or to watching the commercials. Among the men, 16% were planning to watch and were looking forward primarily to the commercials. Among women, 30% were looking forward primarily to the commercials. a) Was this a stratified sample or a blocked experiment? Explain. b) Was the design of the study appropriate for the advertisers’ questions?

Problem 17E What design? Analyze the design of each research example reported. Is it a sample survey, an observational study, or an experiment? If a sample, what are the population, the parameter of interest, and the sampling procedure? If an observational study, was it retrospective or prospective? If an experiment, describe the factors, treatments, randomization, response variable, and any blocking, matching, or blinding that may be present. In each, what kind of conclusions can be reached? The journal Circulation reported that among 1900 people who had heart attacks, those who drank an average of 19 cups of tea a week were 44% more likely than nondrinkers to survive at least 3 years after the attack.

Menopause Researchers studied the herb black cohosh as a treatment for hot flashes caused by menopause. They randomly assigned 318 women aged 55 to 60 who reported at least two hot flashes a day to one of five groups: (1) black cohosh, (2) a multiherb supplement with black cohosh, (3) the multiherb supplement plus advice to consume more soy foods, (4) estrogen replacement therapy, or (5) a placebo. After a year, only the women given estrogen replacement therapy had symptoms different from those of the placebo group. a) What kind of study was this? b) Is that an appropriate choice for this problem? c) Who were the subjects? d) Identify the treatment and response variables.

Problem 20E Honesty Coffee stations in offices often just ask users to leave money in a tray to pay for their coffee, but many people cheat. Researchers at Newcastle University replaced the picture of flowers on the wall behind the coffee station with a picture of staring eyes. They found that the average contribution increased significantly above the well-established standard when people felt they were being watched, even though the eyes were patently not real. (Source: The New York Times 12/10/06) a) Was this a survey, an observational study, or an experiment? How can we tell? b) Identify the variables. c) What does “increased significantly” mean in a statistical sense?

Problem 19RE Save the grapes. Vineyard owners have problems with birds that like to eat the ripening grapes. Some vineyards use scarecrows to try to keep birds away. Others use netting that covers the plants. Owners really would like to know if either method works and, if so, which one is better. One owner has offered to let you use his vineyard this year for an experiment. Propose a design. Carefully indicate how you would set up the experiment, specifying the factor(s) and response variable.

Problem 20RE Bats. It’s generally believed that baseball players can hit the ball farther with aluminum bats than with the traditional wooden ones. Is that true? And, if so, how much farther? Players on your local high school baseball team have agreed to help you find out. Design an appropriate experiment.

Problem 21E What design? Analyze the design of each research example reported. Is it a sample survey, an observational study, or an experiment? If a sample, what are the population, the parameter of interest, and the sampling procedure? If an observational study, was it retrospective or prospective? If an experiment, describe the factors, treatments, randomization, response variable, and any blocking, matching, or blinding that may be present. In each, what kind of conclusions can be reached? The radioactive gas radon, found in some homes, poses a health risk to residents. To assess the level of contamination in their area, a county health department wants to test a few homes. If the risk seems high, they will publicize the results to emphasize the need for home testing. Officials plan to use the local property tax list to randomly choose 25 homes from various areas of the county.

Problem 21RE Diet and blood pressure An experiment that showed that subjects fed the DASH diet were able to lower their blood pressure by an average of 6.7 points compared to a group fed a “control diet.” All meals were prepared by dieticians. a) Why were the subjects randomly assigned to the diets instead of letting people pick what they wanted to eat? ________________ b) Why were the meals prepared by dieticians? ________________ c) Why did the researchers need the control group? If the DASH diet group’s blood pressure was lower at the end of the experiment than at the beginning, wouldn’t that prove the effectiveness of that diet? ________________ d) What additional information would you want to know in order to decide whether an average reduction in blood pressure of 6.7 points was statistically significant?

Problem 22E Read each brief report of statistical research, and identify a) whether it was an observational study or an experiment. If it was an observational study, identify (if possible) b) whether it was retrospective or prospective. c) the subjects studied and how they were selected. d) the parameter of interest. e) the nature and scope of the conclusion the study can reach. If it was an experiment, identify (if possible) b) the subjects studied. c) the factor(s) in the experiment and the number of levels for each. d) the number of treatments. e) the response variable measured. f) the design (completely randomized, blocked, or matched). g) whether it was blind (or double-blind). h) the nature and scope of the conclusion the experiment can reach. Among a group of disabled women aged 65 and older who were tracked for several years, those who had a vitamin B12 deficiency were twice as likely to suffer severe depression as those who did not. (Source: American Journal of Psychiatry 157 [2000]: 715)

Problem 23E Read each brief report of statistical research, and identify a) whether it was an observational study or an experiment. If it was an observational study, identify (if possible) b) whether it was retrospective or prospective. c) the subjects studied and how they were selected. d) the parameter of interest. e) the nature and scope of the conclusion the study can reach. If it was an experiment, identify (if possible) b) the subjects studied. c) the factor(s) in the experiment and the number of levels for each. d) the number of treatments. e) the response variable measured. f) the design (completely randomized, blocked, or matched). g) whether it was blind (or double-blind). h) the nature and scope of the conclusion the experiment can reach. In a test of roughly 200 men and women, those with moderately high blood pressure (averaging 164/89 mm Hg) did worse on tests of memory and reaction time than those with normal blood pressure. (Source: Hypertension 36 [2000]: 1079)

Problem 22RE Mozart Will listening to a Mozart piano sonata make you smarter? In a 1995 study published in the journal Psychological Science, Rauscher, Shaw, and Ky reported that when students were given a spatial reasoning section of a standard IQ test, those who listened to Mozart for 10 minutes improved their scores more than those who simply sat quietly. a) These researchers said the differences were statistically significant. Explain what that means in context. ________________ b) Steele, Bass, and Crook tried to replicate the original study. In their study, also published in Psychological Science (1999), the subjects were 125 college students who participated in the experiment for course credit. Subjects first took the test. Then they were assigned to one of three groups: listening to a Mozart piano sonata, listening to music by Philip Glass, and sitting for 10 minutes in silence. Three days after the treatments, they were retested. Draw a diagram displaying the design of this experiment. ________________ c) These boxplots show the differences in score before and after treatment for the three groups. Did the Mozart group show improvement? ________________ d) Do you think the results prove that listening to Mozart is beneficial? Explain.

Problem 23RE Tips In restaurants, servers rely on tips as a major source of income. Does serving candy after the meal produce larger tips? To find out, two waiters determined randomly whether or not to give candy to 92 dining parties. They recorded the sizes of the tips and reported that guests getting candy tipped an average of 17.8% of the bill, compared with an average tip of only 15.1% from those who got no candy. (Source: “Sweetening the Till: The Use of Candy to Increase Restaurant Tipping.” Journal of Applied Social Psychology 32, no. 2 [2002]: 300–309) a) Was this an experiment or an observational study? Explain. b) Is it reasonable to conclude that the candy caused guests to tip more? Explain. c) The researchers said the difference was statistically significant. Explain in this context what that means.

Problem 24RE NBA draft lottery. Professional basketball teams hold a “draft” each year in which they get to pick the best available college and high school players. In an effort to promote competition, teams with the worst records get to pick first, theoretically allowing them to add better players. To combat the fear that teams with no chance to make the playoffs might try to get better draft picks by intentionally losing late-season games, the NBA’s Board of Governors adopted a weighted lottery system in 1990. Under this system, the 11 teams that did not make the playoffs were eligible for the lottery. The NBA prepared 66 cards, each naming one of the teams. The team with the worst win-loss record was named on 11 of the cards, the second-worst team on 10 cards, and so on, with the team having the best record among the nonplayoff clubs getting only one chance at having the first pick. The cards were mixed, then drawn randomly to determine the order in which the teams could draft players. Suppose there are two exceptional players available in this year’s draft and your favorite team had the third-worst record. Use a simulation to find out how likely it is that your team gets to pick first or second. Describe your simulation carefully.

What’s the design? Read each brief report of statistical research, and identify a) whether it was an observational study or an experiment. If it was an observational study, identify (if possible) b) whether it was retrospective or prospective. c) the subjects studied and how they were selected. d) the parameter of interest. e) the nature and scope of the conclusion the study can reach. If it was an experiment, identify (if possible) b) the subjects studied. c) the factor(s) in the experiment and the number of levels for each. d) the number of treatments. e) the response variable measured. f) the design (completely randomized, blocked, or matched). g) whether it was blind (or double-blind). h) the nature and scope of the conclusion the experiment can reach. Is diet or exercise effective in combating insomnia? Some believe that cutting out desserts can help alleviate the problem, while others recommend exercise. Forty volunteers suffering from insomnia agreed to participate in a month-long test. Half were randomly assigned to a special no-desserts diet; the others continued desserts as usual. Half of the people in each of these groups were randomly assigned to an exercise program, while the others did not exercise. Those who ate no desserts and engaged in exercise showed the most improvement.

Problem 25E Read each brief report of statistical research, and identify a) whether it was an observational study or an experiment. If it was an observational study, identify (if possible) b) whether it was retrospective or prospective. c) the subjects studied and how they were selected. d) the parameter of interest. e) the nature and scope of the conclusion the study can reach. If it was an experiment, identify (if possible) b) the subjects studied. c) the factor(s) in the experiment and the number of levels for each. d) the number of treatments. e) the response variable measured. f) the design (completely randomized, blocked, or matched). g) whether it was blind (or double-blind). h) the nature and scope of the conclusion the experiment can reach. After menopause, some women take supplemental estrogen. There is some concern that if these women also drink alcohol, their estrogen levels will rise too high. Twelve volunteers who were receiving supplemental estrogen were randomly divided into two groups, as were 12 other volunteers not on estrogen. In each case, one group drank an alcoholic beverage, the other a nonalcoholic beverage. An hour later, everyone’s estrogen level was checked. Only those on supplemental estrogen who drank alcohol showed a marked increase.

Problem 26E Read each brief report of statistical research, and identify a) whether it was an observational study or an experiment. If it was an observational study, identify (if possible) b) whether it was retrospective or prospective. c) the subjects studied and how they were selected. d) the parameter of interest. e) the nature and scope of the conclusion the study can reach. If it was an experiment, identify (if possible) b) the subjects studied. c) the factor(s) in the experiment and the number of levels for each. d) the number of treatments. e) the response variable measured. f) the design (completely randomized, blocked, or matched). g) whether it was blind (or double-blind). h) the nature and scope of the conclusion the experiment can reach. Researchers have linked an increase in the incidence of breast cancer in Italy to dioxin released by an industrial accident in 1976. The study identified 981 women who lived near the site of the accident and were under age 40 at the time. Fifteen of the women had developed breast cancer at an unusually young average age of 45. Medical records showed that they had heightened concentrations of dioxin in their blood and that each tenfold increase in dioxin level was associated with a doubling of the risk of breast cancer. (Source: Science News, Aug. 3, 2002)

Problem 25RE Timing In August 2011, a Sodahead.com voluntary response poll asked site visitors, “Obama is on Vacation Again: Does He Have the Worst Timing Ever?” 56% of the 629 votes were for “Yes.” During the week of the poll, a 5.8 earthquake struck near Washington, D.C., and Hurricane Irene made its way up the East coast. What types of bias may be present in the results of the poll?

Laundry An experiment to test a new laundry detergent, SparkleKleen, is being conducted by a consumer advocate group. They would like to compare its performance with that of a laboratory standard detergent they have used in previous experiments. They can stain 16 swatches of cloth with 2 tsp of a common staining compound and then use a well-calibrated optical scanner to detect the amount of the stain left after washing. To save time in the experiment, several suggestions have been made. Comment on the possible merits and drawbacks of each one. a) Since data for the laboratory standard detergent are already available from previous experiments, for this experiment wash all 16 swatches with SparkleKleen, and compare the results with the previous data. b) Use both detergents with eight separate runs each, but to save time, use only a 10-second wash time with very hot water. c) To ease bookkeeping, first run all of the standard detergent washes on eight swatches, then run all of the SparkleKleen washes on the other eight swatches. d) Rather than run the experiment, use data from the company that produced SparkleKleen, and compare them with past data from the standard detergent.

What’s the design? Read each brief report of statistical research, and identify a) whether it was an observational study or an experiment. If it was an observational study, identify (if possible) b) whether it was retrospective or prospective. c) the subjects studied and how they were selected. d) the parameter of interest. e) the nature and scope of the conclusion the study can reach. If it was an experiment, identify (if possible) b) the subjects studied. c) the factor(s) in the experiment and the number of levels for each. d) the number of treatments. e) the response variable measured. f) the design (completely randomized, blocked, or matched). g) whether it was blind (or double-blind). h) the nature and scope of the conclusion the experiment can reach. In 2002, the journal Science reported that a study of women in Finland indicated that having sons shortened the life spans of mothers by about 34 weeks per son, but that daughters helped to lengthen the mothers’ lives. The data came from church records from the period 1640 to 1870.

Problem 28E Read each brief report of statistical research, and identify a) whether it was an observational study or an experiment. If it was an observational study, identify (if possible) b) whether it was retrospective or prospective. c) the subjects studied and how they were selected. d) the parameter of interest. e) the nature and scope of the conclusion the study can reach. If it was an experiment, identify (if possible) b) the subjects studied. c) the factor(s) in the experiment and the number of levels for each. d) the number of treatments. e) the response variable measured. f) the design (completely randomized, blocked, or matched). g) whether it was blind (or double-blind). h) the nature and scope of the conclusion the experiment can reach. Scientists at a major pharmaceutical firm investigated the effectiveness of an herbal compound to treat the common cold. They exposed each subject to a cold virus, then gave him or her either the herbal compound or a sugar solution known to have no effect on colds. Several days later, they assessed the patient’s condition, using a cold severity scale ranging from 0 to 5. They found no evidence of benefits associated with the compound.

Problem 27RE Security. There are 20 first-class passengers and 120 coach passengers scheduled on a flight. In addition to the usual security screening, 10% of the passengers will be subjected to a more complete search. a) Describe a sampling strategy to randomly select those to be searched. ________________ b) Here is the first-class passenger list and a set of random digits. Select two passengers to be searched, carefully demonstrating your process. 65436 71127 04879 41516 20451 02227 94769 23593 Bergman Cox Fontana Perl Bowman DeLara Forester Rabkin Burkhauser Delli-Bovi Frongillo Roufaiel Castillo Dugan Furnas Swafford Clancy Febo LePage Testut ________________ c) Explain how you would use a random number table to select the coach passengers to be searched.

Problem 28RE Profiling? Among the 20 first-class passengers on the flight described in Exercise, there were four businessmen from the Middle East. Two of them were the two passengers selected to be searched. They complained of profiling, but the airline claims that the selection was random. What do you think? Support your conclusion with a simulation. Exercise Security. There are 20 first-class passengers and 120 coach passengers scheduled on a flight. In addition to the usual security screening, 10% of the passengers will be subjected to a more complete search. a) Describe a sampling strategy to randomly select those to be searched. ________________ b) Here is the first-class passenger list and a set of random digits. Select two passengers to be searched, carefully demonstrating your process. 65436 71127 04879 41516 20451 02227 94769 23593 Bergman Cox Fontana Perl Bowman DeLara Forester Rabkin Burkhauser Delli-Bovi Frongillo Roufaiel Castillo Dugan Furnas Swafford Clancy Febo LePage Testut ________________ c) Explain how you would use a random number table to select the coach passengers to be searched.

Problem 29RE Full moon It’s a common belief that people behave strangely when there’s a full moon and that as a result police and emergency rooms are busier than usual. Design a way you could find out whether there is any merit to this belief. Will you use an observational study or an experiment? Why?

Problem 30E Read each brief report of statistical research, and identify a) whether it was an observational study or an experiment. If it was an observational study, identify (if possible) b) whether it was retrospective or prospective. c) the subjects studied and how they were selected. d) the parameter of interest. e) the nature and scope of the conclusion the study can reach. If it was an experiment, identify (if possible) b) the subjects studied. c) the factor(s) in the experiment and the number of levels for each. d) the number of treatments. e) the response variable measured. f) the design (completely randomized, blocked, or matched). g) whether it was blind (or double-blind). h) the nature and scope of the conclusion the experiment can reach. Some people who race greyhounds give the dogs large doses of vitamin C in the belief that the dogs will run faster. Investigators at the University of Florida tried three different diets in random order on each of five racing greyhounds. They were surprised to find that when the dogs ate high amounts of vitamin C they ran more slowly. (Source: Science News, July 20, 2002)

Problem 30RE Wine A 2001 Danish study published in the Archives of Internal Medicine casts significant doubt on suggestions that adults who drink wine have higher levels of “good” cholesterol and fewer heart attacks. These researchers followed a group of individuals born at a Copenhagen hospital between 1959 and 1961 for 40 years. Their study found that in this group the adults who drank wine were richer and better educated than those who did not. a) What kind of study was this? ________________ b) It is generally true that people with high levels of education and high socioeconomic status are healthier than others. How does this call into question the supposed health benefits of wine? ________________ c) Can studies such as these prove causation (that wine helps prevent heart attacks, that drinking wine makes one richer, that being rich helps prevent heart attacks, etc.)? Explain.

Problem 29E What design? Analyze the design of each research example reported. Is it a sample survey, an observational study, or an experiment? If a sample, what are the population, the parameter of interest, and the sampling procedure? If an observational study, was it retrospective or prospective? If an experiment, describe the factors, treatments, randomization, response variable, and any blocking, matching, or blinding that may be present. In each, what kind of conclusions can be reached? Some doctors have expressed concern that men who have vasectomies seemed more likely to develop prostate cancer. Medical researchers used a national cancer registry to identify 923 men who had had prostate cancer and 1224 men of similar ages who had not. Roughly one quarter of the men in each group had undergone a vasectomy, many more than 25 years before the study. The study’s authors concluded that there is strong evidence that having the operation presents no long-term risk for developing prostate cancer. (Source: Science News, July 20, 2002)

What’s the design? Read each brief report of statistical research, and identify a) whether it was an observational study or an experiment. If it was an observational study, identify (if possible) b) whether it was retrospective or prospective. c) the subjects studied and how they were selected. d) the parameter of interest. e) the nature and scope of the conclusion the study can reach. If it was an experiment, identify (if possible) b) the subjects studied. c) the factor(s) in the experiment and the number of levels for each. d) the number of treatments. e) the response variable measured. f) the design (completely randomized, blocked, or matched). g) whether it was blind (or double-blind). h) the nature and scope of the conclusion the experiment can reach. Some people claim they can get relief from migraine headache pain by drinking a large glass of ice water. Researchers plan to enlist several people who suffer from migraines in a test. When a participant experiences a migraine headache, he or she will take a pill that may be a standard pain reliever or a placebo. Half of each group will also drink ice water. Participants will then report the level of pain relief they experience.

Problem 31RE Smoking and Alzheimer’s Medical studies indicate that smokers are less likely to develop Alzheimer’s disease than people who never smoked. a) Does this prove that smoking may offer some protection against Alzheimer’s? Explain. b) Offer an alternative explanation for this association. c) How would you conduct a study to investigate this?

Problem 32RE Antacids A researcher wants to compare the performance of three types of antacid in volunteers suffering from acid reflux disease. Because men and women may react differently to this medication, the subjects are split into two groups, by sex. Subjects in each group are randomly assigned to take one of the antacids or to take a sugar pill made to look the same. The subjects will rate their level of discomfort 30 minutes after eating. a) What kind of design is this? b) The experiment uses volunteers rather than a random sample of all people suffering from acid reflux disease. Does this make the results invalid? Explain. c) How may the use of the placebo confound this experiment? Explain.

Problem 32E Read each brief report of statistical research, and identify a) whether it was an observational study or an experiment. If it was an observational study, identify (if possible) b) whether it was retrospective or prospective. c) the subjects studied and how they were selected. d) the parameter of interest. e) the nature and scope of the conclusion the study can reach. If it was an experiment, identify (if possible) b) the subjects studied. c) the factor(s) in the experiment and the number of levels for each. d) the number of treatments. e) the response variable measured. f) the design (completely randomized, blocked, or matched). g) whether it was blind (or double-blind). h) the nature and scope of the conclusion the experiment can reach. A dog food company wants to compare a new lower calorie food with their standard dog food to see if it’s effective in helping inactive dogs maintain a healthy weight. They have found several dog owners willing to participate in the trial. The dogs have been classified as small, medium, or large breeds, and the company will supply some owners of each size of dog with one of the two foods. The owners have agreed not to feed their dogs anything else for a period of 6 months, after which the dogs’ weights will be checked.

Problem 34E What design? Analyze the design of each research example reported. Is it a sample survey, an observational study, or an experiment? If a sample, what are the population, the parameter of interest, and the sampling procedure? If an observational study, was it retrospective or prospective? If an experiment, describe the factors, treatments, randomization, response variable, and any blocking, matching, or blinding that may be present. In each, what kind of conclusions can be reached? Tests of gene therapy on laboratory rats have raised hopes of stopping the degeneration of tissue that characterizes chronic heart failure. Researchers at the University of California, San Diego, used hamsters with cardiac disease, randomly assigning 30 to receive the gene therapy and leaving the other 28 untreated. Five weeks after treatment the gene therapy group’s heart muscles stabilized, while those of the untreated hamsters continued to weaken. (Source: Science News, July 27, 2002)

Pubs In England, a Leeds University researcher said that the local watering hole’s welcoming atmosphere helps men get rid of the stresses of modern life and is vital for their psychological well-being. Author of the report, Dr. Colin Gill, said rather than complain, women should encourage men to “pop out for a swift half.” “Pub-time allows men to bond with friends and colleagues,” he said. “Men need break-out time as much as women and are mentally healthier for it.” Gill added that men might feel unfulfilled or empty if they had not been to the pub for a week. The report, commissioned by alcohol-free beer brand Kaliber, surveyed 900 men on their reasons for going to the pub. More than 40% said they went for the conversation, with relaxation and a friendly atmosphere being the other most common reasons. Only 1 in 10 listed alcohol as the overriding reason. Let’s examine this news story from a statistical perspective. a) What are the W’s: Who, What, When, Where, Why, How? b) What population does the researcher think the study applies to? c) What is the most important thing about the selection process that the article does not tell us? d) How do you think the 900 respondents were selected? (Name a method of drawing a sample that is likely to have been used.) e) Do you think the report that only 10% of respondents listed alcohol as an important reason for going to the pub might be a biased result? Why?

Problem 33RE Swimming Recently, a group of adults who swim regularly for exercise were evaluated for depression. It turned out that these swimmers were less likely to be depressed than the general population. The researchers said the difference was statistically significant. a) What does “statistically significant” mean in this context? ________________ b) Is this an experiment or an observational study? Explain. ________________ c) News reports claimed this study proved that swimming can prevent depression. Explain why this conclusion is not justified by the study. Include an example of a possible lurking variable. ________________ d) But perhaps it is true. We wonder if exercise can ward off depression, and whether anaerobic exercise (like weight training) is as effective as aerobic exercise (like swimming). We find 120 volunteers not currently engaged in a regular program of exercise. Design an appropriate experiment.

Problem 33E Alcohol and estrogen After menopause, some women take supplemental estrogen. There is some concern that if these women also drink alcohol, their estrogen levels will rise too high. Twelve volunteers who were receiving supplemental estrogen were randomly divided into two groups, as were 12 other volunteers not on estrogen. In each case, one group drank an alcoholic beverage, the other a nonalcoholic beverage. An hour later, everyone’s estrogen level was checked. Only those on supplemental estrogen who drank alcohol showed a marked increase.

Problem 35E Omega-3 Exercise 21 describes an experiment that showed that high doses of omega-3 fats might be of benefit to people with bipolar disorder. The experiment involved a control group of subjects who received a placebo. Why didn’t the experimenters just give everyone the omega-3 fats to see if they improved? Exercise 21: Read each brief report of statistical research, and identify a) whether it was an observational study or an experiment. If it was an observational study, identify (if possible) b) whether it was retrospective or prospective. c) the subjects studied and how they were selected. d) the parameter of interest. e) the nature and scope of the conclusion the study can reach. If it was an experiment, identify (if possible) b) the subjects studied. c) the factor(s) in the experiment and the number of levels for each. d) the number of treatments. e) the response variable measured. f) the design (completely randomized, blocked, or matched). g) whether it was blind (or double-blind). h) the nature and scope of the conclusion the experiment can reach. Over a 4-month period, among 30 people with bipolar disorder, patients who were given a high dose (10 g/day) of omega-3 fats from fish oil improved more than those given a placebo. (Source: Archives of General Psychiatry 56 [1999]: 407)

Problem 36E Tossing and turning Is diet or exercise effective in combating insomnia? Some believe that cutting out desserts can help alleviate the problem, while others recommend exercise. Forty volunteers suffering from insomnia agreed to participate in a month-long test. Half were randomly assigned to a special no-desserts diet; the others continued desserts as usual. Half of the people in each of these groups were randomly assigned to an exercise program, while the others did not exercise. Those who ate no desserts and engaged in exercise showed the most improvement.

Age and party 2008 The Pew Research Center collected data from national exits polls conducted by NBC News after the 2008 presidential election. The following table shows information regarding voter age and party preference: a) What sampling strategy do you think the pollsters used? Explain. b) What percentage of the people surveyed were Democrats? c) Do you think this is a good estimate of the percentage of voters in the United States who are registered Democrats? Why or why not? d) In creating this sample design, what question do you think the pollsters were trying to answer?

Omega-3, revisited Exercises 21 and 35 describe an experiment investigating a dietary approach to treating bipolar disorder. Researchers randomly assigned 30 subjects to two treatment groups, one group taking a high dose of omega-3 fats and the other a placebo. a) Why was it important to randomize in assigning the subjects to the two groups? b) What would be the advantages and disadvantages of using 100 subjects instead of 30?

Save the grapes. Vineyard owners have problems with birds that like to eat the ripening grapes. Some vineyards use scarecrows to try to keep birds away. Others use netting that covers the plants. Owners really would like to know if either method works and, if so, which one is better. One owner has offered to let you use his vineyard this year for an experiment. Propose a design. Carefully indicate how you would set up the experiment, specifying the factor(s) and response variable.

Problem 36RE Reading Some schools teach reading using phonics (the sounds made by letters) and others using whole language (word recognition). Suppose a school district wants to know which method works better. Suggest a design for an appropriate experiment.

Insomnia, again Exercises 24 and 36 describe an experiment investigating the effectiveness of exercise in combating insomnia. Researchers randomly assigned half of the 40 volunteers to an exercise program. a) Why was it important to randomize in deciding who would exercise? b) What would be the advantages and disadvantages of using 100 subjects instead of 40?

Bats It’s generally believed that baseball players can hit the ball farther with aluminum bats than with the traditional wooden ones. Is that true? And, if so, how much farther? Players on your local high school baseball team have agreed to help you find out. Design an appropriate experiment.

Problem 39E What design? Analyze the design of each research example reported. Is it a sample survey, an observational study, or an experiment? If a sample, what are the population, the parameter of interest, and the sampling procedure? If an observational study, was it retrospective or prospective? If an experiment, describe the factors, treatments, randomization, response variable, and any blocking, matching, or blinding that may be present. In each, what kind of conclusions can be reached? A soft-drink manufacturer must be sure the bottle caps on the soda are fully sealed and will not come off easily. Inspectors pull a few bottles off the production line at regular intervals and test the caps. If they detect any problems, they will stop the bottling process to adjust or repair the machine that caps the bottles.

Problem 40RE Beetles Hoping to learn how to control crop damage by a certain species of beetle, a researcher plans to test two different pesticides in small plots of corn. A few days after application of the chemicals, he’ll check the number of beetle larvae found on each plant. The researcher wants to know whether either pesticide works and whether there is a significant difference in effectiveness between them. Design an appropriate experiment.

Problem 39RE Acupuncture Research reported in 2008 brings to light the effectiveness of treating chronic lower back pain with different methods. One-third of nearly 1200 volunteers were administered conventional treatment (drugs, physical therapy, and exercise). The remaining patients got 30-minute acupuncture sessions. Half of these patients were punctured at sites suspected of being useful and half received needles at other spots on their bodies. Comparable shares of each acupuncture group, roughly 45%, reported decreased back pain for at least six months after their sessions ended. This was almost twice as high as those receiving the conventional therapy, leading the researchers to conclude that results were statistically significant. a) Why did the researchers feel it was necessary to have some of the patients undergo a “fake” acupunture? b) Because patients had to consent to participate in this experiment, the subjects were essentially selfselected— a kind of voluntary response group. Explain why that does not invalidate the findings of the experiment. c) What does “statistically significant” mean in the context of this experiment?

Problem 40E Dioxin Researchers have linked an increase in the incidence of breast cancer in Italy to dioxin released by an industrial accident in 1976. The study identified 981 women who lived near the site of the accident and were under age 40 at the time. Fifteen of the women had developed breast cancer at an unusually young average age of 45. Medical records showed that they had heightened concentrations of dioxin in their blood and that each tenfold increase in dioxin level was associated with a doubling of the risk of breast cancer. (Science News, Aug. 3, 2002)

Problem 41E Injuries Exercise 33 describes an experiment that studies hamstring injuries. Describe a strategy to randomly assign injured athletes to the two exercise programs. What should be done if one of the athletes says he’d prefer the other program? Exercise 33: Read each brief report of statistical research, and identify a) whether it was an observational study or an experiment. If it was an observational study, identify (if possible) b) whether it was retrospective or prospective. c) the subjects studied and how they were selected. d) the parameter of interest. e) the nature and scope of the conclusion the study can reach. If it was an experiment, identify (if possible) b) the subjects studied. c) the factor(s) in the experiment and the number of levels for each. d) the number of treatments. e) the response variable measured. f) the design (completely randomized, blocked, or matched). g) whether it was blind (or double-blind). h) the nature and scope of the conclusion the experiment can reach. Athletes who had suffered hamstring injuries were randomly assigned to one of two exercise programs. Those who engaged in static stretching returned to sports activity in a mean of 15.2 days faster than those assigned to a program of agility and trunk stabilization exercises. (Source: Journal of Orthopaedic & Sports Physical Therapy 34 [March 2004]: 3)

Problem 41RE SAT Prep Can special study courses actually help raise SAT scores? One organization says that the 30 students they tutored achieved an average gain of 60 points when they retook the test. a) Explain why this does not necessarily prove that the special course caused the scores to go up. ________________ b) Propose a design for an experiment that could test the effectiveness of the tutorial course. ________________ c) Suppose you suspect that the tutorial course might be more helpful for students whose initial scores were particularly low. How would this affect your proposed design?

Problem 42E Tomatoes II Describe a strategy to randomly split 24 tomato plants into the three groups for the completely randomized single factor experiment of Exercise 4. Exercise 4: Tomatoes You want to compare the tastiness and juiciness of tomatoes grown with three amounts of a new fertilizer: none, half the recommended amount, and the full recommended amount. You allocate 6 tomato plants to receive each amount of fertilizer, assigning them at random. What are the experimental units? What is the response variable?

Profiling? Among the 20 first-class passengers on the flight described in Exercise 41, there were four businessmen from the Middle East. Two of them were the two passengers selected to be searched. They complained of profiling, but the airline claims that the selection was random. What do you think? Support your conclusion with a simulation.

Problem 43RE Par 4. In theory, a golfer playing a par-4 hole tees off, hitting the ball in the fairway, then hits an approach shot onto the green. The first putt (usually long) probably won’t go in, but the second putt (usually much shorter) should. Sounds simple enough, but how many strokes might it really take? Use a simulation to estimate a pretty good golfer’s score based on these assumptions: • The tee shot hits the fairway 70% of the time. • A first approach shot lands on the green 80% of the time from the fairway, but only 40% of the time otherwise. • Subsequent approach shots land on the green 90% of the time. • The first putt goes in 20% of the time, and subsequent putts go in 90% of the time.

Problem 44E Swimsuits A swimsuit manufacturer wants to test the speed of its newly designed suit. The company designs an experiment by having 6 randomly selected Olympic swimmers swim as fast as they can with their old swimsuit first and then swim the same event again with the new, expensive swimsuit. The company will use the difference in times as the response variable. Criticize the experiment and point out some of the problems with generalizing the results.

Problem 43E Shoes A running-shoe manufacturer wants to test the effect of its new sprinting shoe on 100-meter dash times. The company sponsors 5 athletes who are running the 100-meter dash in the 2012 Summer Olympic games. To test the shoe, it has all 5 runners run the 100-meter dash with a competitor’s shoe and then again with their new shoe. The company uses the difference in times as the response variable. a) Suggest some improvements to the design. b) Why might the shoe manufacturer not be able to generalize the results they find to all runners?

Hamstrings Exercise 33 discussed an experiment to see if the time it took athletes with hamstring injuries to be able to return to sports was different depending on which of two exercise programs they engaged in. a) Explain why it was important to assign the athletes to the two different treatments randomly. b) There was no control group consisting of athletes who did not participate in a special exercise program. Explain the advantage of including such a group. c) How might blinding have been used? d) One group returned to sports activity in a mean of 37.4 days (SD = 27.6 days) and the other in a mean of 22.2 days (SD = 8.3 days). Do you think this difference is statistically significant? Explain.

Diet and blood pressure An experiment showed that subjects fed the DASH diet were able to lower their blood pressure by an average of 6.7 points compared to a group fed a “control diet.” All meals were prepared by dieticians. a) Why were the subjects randomly assigned to the diets instead of letting people pick what they wanted to eat? b) Why were the meals prepared by dieticians? c) Why did the researchers need the control group? If the DASH diet group’s blood pressure was lower at the end of the experiment than at the beginning, wouldn’t that prove the effectiveness of that diet? d) What additional information would you want to know in order to decide whether an average reduction in blood pressure of 6.7 points was statistically significant?

Swimming Recently, a group of adults who swim regularly for exercise were evaluated for depression. It turned out that these swimmers were less likely to be depressed than the general population. The researchers said the difference was statistically significant. a) What does “statistically significant” mean in this context? b) Is this an experiment or an observational study? Explain. c) News reports claimed this study proved that swimming can prevent depression. Explain why this conclusion is not justified by the study. Include an example of a possible lurking variable. d) But perhaps it is true. We wonder if exercise can ward off depression, and whether anaerobic exercise (like weight training) is as effective as aerobic exercise (like swimming). We find 120 volunteers not currently engaged in a regular program of exercise. Design an appropriate experiment.

Problem 51E Dowsing Before drilling for water, many rural homeowners hire a dowser (a person who claims to be able to sense the presence of underground water using a forked stick.) Suppose we wish to set up an experiment to test one dowser’s ability. We get 20 identical containers, fill some with water, and ask him to tell which ones they are. a) How will we randomize this procedure? b) The dowser correctly identifies the contents of 12 out of 20 containers. Do you think this level of success is statistically significant? Explain. c) How many correct identifications (out of 20) would the dowser have to make to convince you that the forked-stick trick works? Explain.

Problem 48E Contrast Baths Contrast bath treatments use the immersion of an injured limb alternately in water of two contrasting temperatures. Those who use the method claim that it can reduce swelling. Researchers compared three treatments: (1) contrast baths and exercise, (2) contrast baths alone, and (3) exercise alone. (Source: R. G. Janssen, D. A. Schwartz, and P.F. Velleman “A Randomized Controlled Study of Contrast Baths on Patients with Carpal Tunnel Syndrome.” Journal of Hand Therapy, 2009). They report the following boxplots comparing the change in hand volume after treatment: a) The researchers conclude that the differences were not statistically significant. Explain what that means in context. b) The title says that the study was randomized and controlled. Explain what that probably means for this study. c) The study did not use a placebo treatment. What was done instead? Do you think that was an appropriate choice? Explain.

Wine A 2001 Danish study published in the Archives of Internal Medicine casts significant doubt on suggestions that adults who drink wine have higher levels of “good” cholesterol and fewer heart attacks. These researchers followed a group of individuals born at a Copenhagen hospital between 1959 and 1961 for 40 years. Their study found that in this group the adults who drank wine were richer and better educated than those who did not. a) What kind of study was this? b) It is generally true that people with high levels of education and high socioeconomic status are healthier than others. How does this call into question the supposed health benefits of wine? c) Can studies such as these prove causation (that wine helps prevent heart attacks, that drinking wine makes one richer, that being rich helps prevent heart attacks, etc.)? Explain.

Problem 44RE The back nine. Use simulations to estimate more golf scores, similar to the procedure in Exercise. a) On a par 3, the golfer hopes the tee shot lands on the green. Assume that the tee shot behaves like the first approach shot described in Exercise. ________________ b) On a par 5, the second shot will reach the green 10% of the time and hit the fairway 60% of the time. If it does not hit the green, the golfer must play an approach shot as described in Exercise. ________________ c) Create a list of assumptions that describe your golfing ability, and then simulate your score on a few holes. Explain your simulation clearly. Exercise Par 4. In theory, a golfer playing a par-4 hole tees off, hitting the ball in the fairway, then hits an approach shot onto the green. The first putt (usually long) probably won’t go in, but the second putt (usually much shorter) should. Sounds simple enough, but how many strokes might it really take? Use a simulation to estimate a pretty good golfer’s score based on these assumptions: • The tee shot hits the fairway 70% of the time. • A first approach shot lands on the green 80% of the time from the fairway, but only 40% of the time otherwise. • Subsequent approach shots land on the green 90% of the time. • The first putt goes in 20% of the time, and subsequent putts go in 90% of the time.

Problem 47E The lottery. Many people spend a lot of money trying to win huge jackpots in state lotteries. Let’s play a simplified version using only the numbers from 1 to 20. You bet on three numbers. The state picks five winning numbers. If your three are all among the winners, you are rich! a) Simulate repeated plays. How long did it take you to win? ________________ b) In real lotteries, there are many more choices (often 54) and you must match all five winning numbers. Explain how these changes affect your chances of hitting the jackpot.

Problem 52E Tips. In restaurants, servers rely on tips as a major source of income. Does serving candy after the meal produce larger tips? To find out, two waiters determined randomly whether or not to give candy to 92 dining parties. They recorded the sizes of the tips and reported that guests getting candy tipped an average of 17.8% of the bill, compared with an average tip of only 15.1% from those who got no candy. (Source: “Sweetening the Till: The Use of Candy to Increase Restaurant Tipping.” Journal of Applied Social Psychology 32, no. 2 [2002]: 300–309) a) Was this an experiment or an observational study? Explain. ________________ b) Is it reasonable to conclude that the candy caused guests to tip more? Explain. ________________ c) The researchers said the difference was statistically significant. Explain in this context what that means.

Reading Some schools teach reading using phonics (the sounds made by letters) and others using whole language (word recognition). Suppose a school district wants to know which method works better. Suggest a design for an appropriate experiment.

Problem 54E Gas mileage Do cars get better gas mileage with premium instead of regular unleaded gasoline? It might be possible to test some engines in a laboratory, but we’d rather use real cars and real drivers in real day-to-day driving, so we get 20 volunteers. Design the experiment.

Problem 55E Weekend deaths A study published in the New England Journal of Medicine (Aug. 2001) suggests that it’s dangerous to enter a hospital on a weekend. During a 10-year period, researchers tracked over 4 million emergency admissions to hospitals in Ontario, Canada. Their findings revealed that patients admitted on weekends had a much higher risk of death than those who went on weekdays. a) The researchers said the difference in death rates was “statistically significant.” Explain in this context what that means. b) What kind of study was this? Explain. c) If you think you’re quite ill on a Saturday, should you wait until Monday to seek medical help? Explain. d) Suggest some possible explanations for this troubling finding.

Shingles A research doctor has discovered a new ointment that she believes will be more effective than the current medication in the treatment of shingles (a painful skin rash). Eight patients have volunteered to participate in the initial trials of this ointment. You are the statistician hired as a consultant to help design an experiment. a) Describe how you will conduct this experiment. b) Suppose the eight patients’ last names start with the letters A to H. Using the random numbers listed below, show which patients you will assign to each treatment. Explain your randomization procedure clearly. 41098 18329 78458 31685 55259 c) Can you make this experiment double-blind? How? d) The initial experiment revealed that males and females may respond differently to the ointment. Further testing of the drug’s effectiveness is now planned, and many patients have volunteered. What changes in your first design, if any, would you make for this second stage of testing?

Problem 57E Laundry. An experiment to test a new laundry detergent, SparkleKleen, is being conducted by a consumer advocate group. They would like to compare its performance with that of a laboratory standard detergent they have used in previous experiments. They can stain 16 swatches of cloth with 2 tsp of a common staining compound and then use a well-calibrated optical scanner to detect the amount of the stain left after washing. To save time in the experiment, several suggestions have been made. Comment on the possible merits and drawbacks of each one. a) Since data for the laboratory standard detergent are already available from previous experiments, for thisexperiment wash all 16 swatches with SparkleKleen, and compare the results with the previous data. ________________ b) Use both detergents with eight separate runs each, but to save time, use only a 10-second wash time with very hot water. ________________ c) To ease bookkeeping, first run all of the standard detergent washes on eight swatches, then run all of the SparkleKleen washes on the other eight swatches. ________________ d) Rather than run the experiment, use data from the company that produced SparkleKleen, and compare them with past data from the standard detergent.

SAT prep Can special study courses actually help raise SAT scores? One organization says that the 30 students they tutored achieved an average gain of 60 points when they retook the test. a) Explain why this does not necessarily prove that the special course caused the scores to go up. b) Propose a design for an experiment that could test the effectiveness of the tutorial course. c) Suppose you suspect that the tutorial course might be more helpful for students whose initial scores were particularly low. How would this affect your proposed design?

Problem 59E Safety switch An industrial machine requires an emergency shutoff switch that must be designed so that it can be easily operated with either hand. Design an experiment to find out whether workers will be able to deactivate the machine as quickly with their left hands as with their right hands. Be sure to explain the role of randomization in your design.

Problem 60E When to stop? You play a game that involves rolling a die. You can roll as many times as you want, and your score is the total for all the rolls. But . . . if you roll a 6 your score is 0 and your turn is over. What might be a good strategy for a game like this? a) One of your opponents decides to roll 4 times, then stop (hoping not to get the dreaded 6 before then). Use a simulation to estimate his average score. ________________ b) Another opponent decides to roll until she gets at least 12 points, then stop. Use a simulation to estimate her average score. ________________ c) Propose another strategy that you would use to play this game. Using your strategy, simulate several turns. Do you think you would beat the two opponents?

Problem 61E Rivets. A company that manufactures rivets believes the shear strength of the rivets they manufacture follows a Normal model with a mean breaking strength of 950 pounds and a standard deviation of 40 pounds. a) What percentage of rivets selected at random will break when tested under a 900-pound load? ________________ b) You’re trying to improve the rivets and want to examine some that fail. Use a simulation to estimate how many rivets you might need to test in order to find three that fail at 900 pounds (or below).