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Stats Data And Models (Subscription) 3rd Edition Richard D De Veaux, Paul D Velleman, David E Bock - Solutions
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
Hamstrings. Exercise 19 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
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
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 2004 Summer Olympic games. To test the shoe, it has all 5 runners run the 100-meter dash with a competitor’s shoe
Tomatoes II. The chapter also described a completely randomized two-factor experiment testing OptiGro fertilizer in conjunction with two different routines for watering the plants. Describe a strategy to randomly assign the 24 tomato plants to the six treatments.
Tomatoes. Describe a strategy to randomly split the 24 tomato plants into the three groups for the chapter’s completely randomized single factor test of OptiGro fertilizer.
Insomnia, at last. Exercises 10, 22, and 24 describe an experiment investigating the effectiveness of exercise in combating insomnia. Suppose some of the 40 subjects had maintained a healthy weight, but others were quite overweight. Why might researchers choose to block the subjects by weight level
Omega-3, finis. Exercises 7, 21, and 23 describe an experiment investigating the effectiveness of omega-3 fats in treating bipolar disorder. Suppose some of the 30 subjects were very active people who walked a lot or got vigorous exercise several times a week, while others tended to be more
Insomnia, again. Exercises 10 and 22 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
Omega-3, revisited. Exercises 7 and 21 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
Insomnia. Exercise 10 describes an experiment showing that exercise helped people sleep better. The experiment involved other groups of subjects who didn’t exercise.Why didn’t the experimenters just have everyone exercise and see if their ability to sleep improved?
Omega-3. Exercise 7 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
Pew Research compared respondents to an ordinary 5-day telephone survey with respondents to a 4-monthlong rigorous survey designed to generate the highest possible response rate. They were especially interested in identifying any variables for which those who responded to the ordinary survey were
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. (Journal of
A dog food company wants to compare a new lowercalorie 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
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
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
The May 4, 2000, issue of Science News reported that, contrary to popular belief, depressed individuals cry no more often in response to sad situations than nondepressed people. Researchers studied 23 men and 48 women with major depression and 9 men and 24 women with no depression. They showed the
They found no evidence of benefits associated with the compound.
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
In 2002 the journal Science reported that a study of women in Finland indicated that having sons shortened the lifespans 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.
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)
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
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
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
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. (Hypertension 36 [2000]: 1079)
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. (American Journal of Psychiatry 157 [2000]: 715)
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. (Archives of General Psychiatry 56 [1999]: 407)
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
Menopause. Researchers studied the herb black cohosh as a treatment for hot flashes caused by menopause.They randomly assigned 351 women aged 45 to 55 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
Super Bowl commercials. When spending large amounts to purchase advertising time, companies want to know what audience they’ll reach. In January 2007, a poll asked 1008 American adults whether they planned to watch the upcoming Super Bowl. Men and women were asked separately whether they were
MS and vitamin D. Multiple sclerosis (MS) is an autoimmune disease that strikes more often the farther people live from the equator. Could vitamin D—which most people get from the sun’s ultraviolet rays—be a factor?Researchers compared vitamin D levels in blood samples from 150 U.S. military
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
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
More sampling methods. Consider each of these situations. Do you think the proposed sampling method is appropriate? Explain.a) We want to know if there is neighborhood support to turn a vacant lot into a playground. We spend a Saturday afternoon going door-to-door in the neighborhood, asking people
Sampling methods. Consider each of these situations.Do you think the proposed sampling method is appropriate? Explain.a) We want to know what percentage of local doctors accept Medicaid patients. We call the offices of 50 doctors randomly selected from local Yellow Pages listings.b) We want to know
A fish story. Concerned about reports of discolored scales on fish caught downstream from a newly sited chemical plant, scientists set up a field station in a shoreline public park. For one week they asked fishermen there to bring any fish they caught to the field station for a brief inspection. At
Quality control. Sammy’s Salsa, a small local company, produces 20 cases of salsa a day. Each case contains 12 jars and is imprinted with a code indicating the date and batch number. To help maintain consistency, at the end of each day, Sammy selects three jars of salsa, weighs the contents, and
Happy workers? Amanufacturing company employs 14 project managers, 48 foremen, and 377 laborers. In an effort to keep informed about any possible sources of employee discontent, management wants to conduct job satisfaction interviews with a sample of employees every month.a) Do you see any
Accounting. Between quarterly audits, a company likes to check on its accounting procedures to address any problems before they become serious. The accounting staff processes payments on about 120 orders each day.The next day, the supervisor rechecks 10 of the transactions to be sure they were
Fuel economy. Occasionally, when I fill my car with gas, I figure out how many miles per gallon my car got. I wrote down those results after six fill-ups in the past few months.Overall, it appears my car gets 28.8 miles per gallon.a) What statistic have I calculated?b) What is the parameter I’m
Arm length. How long is your arm compared with your hand size? Put your right thumb at your left shoulder bone, stretch your hand open wide, and extend your hand down your arm. Put your thumb at the place where your little finger is, and extend down the arm again. Repeat this a third time. Now your
Cell phone survey. What about drawing a random sample only from cell phone exchanges? Discuss the advantages and disadvantages of such a sampling method compared with surveying randomly generated telephone numbers from non–cell phone exchanges. Do you think these advantages and disadvantages have
Phone surveys. Any time we conduct a survey, we must take care to avoid undercoverage. Suppose we plan to select 500 names from the city phone book, call their homes between noon and 4 p.m., and interview whoever answers, anticipating contacts with at least 200 people.a) Why is it difficult to use
More survey questions. Examine each of the following questions for possible bias. If you think the question is biased, indicate how and propose a better question.a) Do you think high school students should be required to wear uniforms?b) Given humanity’s great tradition of exploration, do you
Survey questions. Examine each of the following questions for possible bias. If you think the question is biased, indicate how and propose a better question.a) Should companies that pollute the environment be compelled to pay the costs of cleanup?b) Given that 18-year-olds are old enough to vote
Banning ephedra. An online poll at a website asked:A nationwide ban of the diet supplement ephedra went into effect recently. The herbal stimulant has been linked to 155 deaths and many more heart attacks and strokes. Ephedra manufacturer NVE Pharmaceuticals, claiming that the FDA lacked proof that
Wording the survey. Two members of the PTA committee in Exercises 17 and 18 have proposed different questions to ask in seeking parents’ opinions.Question 1: Should elementary school–age children have to pass high-stakes tests in order to remain with their classmates?Question 2: Should schools
Playground, act two. The survey described in Exercise 20 asked, Many people believe this playground is too small and in need of repair. Do you think the playground should be repaired and expanded even if that means raising the entrance fee to the park?Describe two ways this question may lead to
Roller coasters. An amusement park has opened a new roller coaster. It is so popular that people are waiting for up to 3 hours for a 2-minute ride. Concerned about how patrons (who paid a large amount to enter the park and ride on the rides) feel about this, they survey every 10th person on the
Playground. Some people have been complaining that the children’s playground at a municipal park is too small and is in need of repair. Managers of the park decide to survey city residents to see if they believe the playground should be rebuilt. They hand out questionnaires to parents who bring
Churches. For your political science class, you’d like to take a survey from a sample of all the Catholic Church members in your city. A list of churches shows 17 Catholic churches within the city limits. Rather than try to obtain a list of all members of all these churches, you decide to pick 3
Four new sampling strategies have been proposed to help the PTA determine whether parents favor requiring elementary students to pass a test in order to be promoted to the next grade. For each, indicate what kind of sampling strategy is involved and what (if any) biases might result.a) Run a poll
Let’s revisit the school system described in Exercise
Parent opinion, part
In a large city school system with 20 elementary schools, the school board is considering the adoption of a new policy that would require elementary students to pass a test in order to be promoted to the next grade. The PTA wants to find out whether parents agree with this plan. Listed below are
Parent opinion, part
Another mistaken poll. Prior to the mayoral election discussed in Exercise 15, the newspaper also conducted a poll. The paper surveyed a random sample of registered voters stratified by political party, age, sex, and area of residence. This poll predicted that Amabo would win the election with 52%
Mistaken poll. A local TV station conducted a“PulsePoll” about the upcoming mayoral election.Evening news viewers were invited to phone in their votes, with the results to be announced on the late-night news. Based on the phone calls, the station predicted that Amabo would win the election with
Dairy inspectors visit farms unannounced and take samples of the milk to test for contamination. If the milk is found to contain dirt, antibiotics, or other foreign matter, the milk will be destroyed and the farm reinspected until purity is restored.
A company packaging snack foods maintains quality control by randomly selecting 10 cases from each day’s production and weighing the bags. Then they open one bag from each case and inspect the contents.
State police set up a roadblock to estimate the percentage of cars with up-to-date registration, insurance, and safety inspection stickers. They usually find problems with about 10% of the cars they stop.
The Environmental Protection Agency took soil samples at 16 locations near a former industrial waste dump and checked each for evidence of toxic chemicals. They found no elevated levels of any harmful substances.
Hoping to learn what issues may resonate with voters in the coming election, the campaign director for a mayoral candidate selects one block from each of the city’s election districts. Staff members go there and interview all the residents they can find.
Researchers waited outside a bar they had randomly selected from a list of such establishments. They stopped every 10th person who came out of the bar and asked whether he or she thought drinking and driving was a serious problem.
A question posted on the Lycos website on 18 June 2000 asked visitors to the site to say whether they thought that marijuana should be legally available for medicinal purposes. (www.lycos.com)
Consumers Union asked all subscribers whether they had used alternative medical treatments and, if so, whether they had benefited from them. For almost all of the treatments, approximately 20% of those responding reported cures or substantial improvement in their condition.
Gallup World. At its website (www.gallupworldpoll.com)the Gallup World Poll describes their methods. After one report they explained:Results are based on face-to-face interviews with randomly selected national samples of approximately 1,000 adults, aged 15 and older, who live permanently in each of
Gallup. At its website (www.gallup.com) the Gallup Poll publishes results of a new survey each day. Scroll down to the end, and you’ll find a statement that includes words such as these:Results are based on telephone interviews with 1,008 national adults, aged 18 and older, conducted April 2–5,
Drug tests. Major League Baseball tests players to see whether they are using performance-enhancing drugs.Officials select a team at random, and a drug-testing crew shows up unannounced to test all 40 players on the team. Each testing day can be considered a study of drug use in Major League
Emoticons. The website www.gamefaqs.com asked, as their question of the day to which visitors to the site were invited to respond, “Do you ever use emoticons when you type online?” Of the 87,262 respondents, 27% said that they did not use emoticons. ;-(a) What kind of sample was this?b) How
Student center survey. For their class project, a group of Statistics students decide to survey the student body to assess opinions about the proposed new student center.Their sample of 200 contained 50 first-year students, 50 sophomores, 50 juniors, and 50 seniors.a) Do you think the group was
Roper. Through their Roper Reports Worldwide, GfK Roper conducts a global consumer survey to help multinational companies understand different consumer attitudes throughout the world. Within 30 countries, the researchers interview 1000 people aged 13–65. Their samples are designed so that they
Cell phones. A proud legislator claims that your state’s new law against talking on a cell phone while driving has reduced cell phone use to less than 12% of all drivers. While waiting for your bus the next morning, you notice that 4 of the 10 people who drive by are using their cell phones. Does
Job discrimination? A company with a large sales staff announces openings for three positions as regional managers. Twenty-two of the current salespersons apply, 12 men and 10 women. After the interviews, when the company announces the newly appointed managers, all three positions go to women. The
Second team. Suppose the couples in Exercise 37 choose the teams by having one member of each couple write their names on the cards and the other people each pick a card at random. How likely is it that every person will be teamed with someone other than the person he or she came with?
Teammates. Four couples at a dinner party play a board game after the meal. They decide to play as teams of two and to select the teams randomly. All eight people write their names on slips of paper. The slips are thoroughly mixed, then drawn two at a time. How likely is it that every person will
The World Series. The World Series ends when a team wins 4 games. Suppose that sports analysts consider one team a bit stronger, with a 55% chance to win any individual game. Estimate the likelihood that the underdog wins the series.
The hot hand. A basketball player with a 65% shooting percentage has just made 6 shots in a row. The announcer says this player “is hot tonight! She’s in the zone!” Assume the player takes about 20 shots per game.Is it unusual for her to make 6 or more shots in a row during a game?
Parcheesi. You are three spaces from a win in Parcheesi.On each turn, you will roll two dice. To win, you must roll a total of 3 or roll a 3 on one of the dice. How many turns might you expect this to take?
Dice game. You are playing a children’s game in which the number of spaces you get to move is determined by the rolling of a die. You must land exactly on the final space in order to win. If you are 10 spaces away, how many turns might it take you to win?
A bigger family. Suppose a couple will continue having children until they have at least two children of each sex(two boys and two girls). How many children might they expect to have?
The family. Many couples want to have both a boy and a girl. If they decide to continue to have children until they have one child of each sex, what would the average family size be? Assume that boys and girls are equally likely.
Find the ace. A new electronics store holds a contest to attract shoppers. Once an hour someone in the store is chosen at random to play the Music Game. Here’s how it works: An ace and four other cards are shuffled and placed face down on a table. The customer gets to turn cards over one at a
Free groceries. To attract shoppers, a supermarket runs a weekly contest that involves “scratch-off” cards. With each purchase, customers get a card with a black spot obscuring a message. When the spot is scratched away, most of the cards simply say, “Sorry—please try again.” But during
Blood donors. A person with type O-positive blood can receive blood only from other type O donors. About 44%of the U.S. population has type O blood. At a blood drive, how many potential donors do you expect to examine in order to get three units of type O blood?
Basketball strategy. Late in a basketball game, the team that is behind often fouls someone in an attempt to get the ball back. Usually the opposing player will get to shoot foul shots “one and one,” meaning he gets a shot, and then a second shot only if he makes the first one.Suppose the
Still learning? As in Exercise 25, assume that your chance of passing the driver’s test is 34% the first time and 72% for subsequent retests. Estimate the percentage of those tested who still do not have a driver’s license after two attempts.
Driving test. You are about to take the road test for your driver’s license. You hear that only 34% of candidates pass the test the first time, but the percentage rises to 72% on subsequent retests. Estimate the average number of tests drivers take in order to get a license. Your simulation
Play the winner? Another strategy for beating the lottery is the reverse of the system described in Exercise 23.Simulate the simplified lottery described in Exercise 21.Each time, bet the number that just turned up. The website suggests that this method should do worse.Does it? Play many games and
It evens out in the end. The “beat the lottery” website of Exercise 21 notes that in the long run we expect each value to turn up about the same number of times. That leads to their recommended strategy. First, watch the lottery for a while, recording the winners. Then bet the value that has
Play many games. What proportion of the time do you win?
Random is as random does. The “beat the lottery”website discussed in Exercise 21 suggests that because lottery numbers are random, it is better to select your bet randomly. For the same simple lottery in Exercise 21(random values from 0 to 9), generate each bet by choosing a separate random
Beat the lottery. Many states run lotteries to raise money. Awebsite advertises that it knows “how to increase YOUR chances of Winning the Lottery.” They offer several systems and criticize others as foolish. One system is called Lucky Numbers. People who play the Lucky Numbers system just pick
Lucky guessing? A friend of yours who took the multiple choice quiz in Exercise 19 got all 6 questions right, but now claims to have guessed blindly on every question. If each question offered 4 possible answers, do you believe her? Explain, basing your argument on a simulation involving at least
Multiple choice. You take a quiz with 6 multiple choice questions. After you studied, you estimated that you would have about an 80% chance of getting any individual question right. What are your chances of getting them all right? Use at least 20 trials.
Cereal, again. Suppose you really want the LeBron James picture. How many boxes of cereal do you need to buy to be pretty sure of getting at least one? Your simulation should use at least 10 trials.
Cereal. In the chapter’s example, 20% of the cereal boxes contained a picture of LeBron James, 30% David Beckham, and the rest Serena Williams. Suppose you buy five boxes of cereal. Estimate the probability that you end up with a complete set of the pictures. Your simulation should have at least
Two pair or three of a kind? When drawing five cards randomly from a deck, which is more likely, two pairs or three of a kind? A pair is exactly two of the same denomination.Three of a kind is exactly 3 of the same denomination.(Don’t count three 8’s as a pair—that’s 3 of a kind. And
Election. You’re pretty sure that your candidate for class president has about 55% of the votes in the entire school.But you’re worried that only 100 students will show up to vote. How often will the underdog (the one with 45%support) win? To find out, you set up a simulation.a) Describe how
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