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inferential statistics
Stats Modeling The World AP Edition Grades 9-12 3rd Edition David E. Bock, Paul F. Velleman, Richard D. De Veaux - Solutions
Roulette. A casino claims that its roulette wheel is truly random. What should that claim mean?
Sample spaces. For each of the following, list the sample space and tell whether you think the events are equally likely:a) Roll two dice; record the sum of the numbers.b) A family has 3 children; record each child s sex in order of birth.c) Toss four coins; record the number of tails.d) Toss a
Sample spaces. For each of the following, list the sample space and tell whether you think the events are equally likely:a) Toss 2 coins; record the order of heads and tails.b) A family has 3 children; record the number of boys.c) Flip a coin until you get a head or 3 consecutive tails.d) Roll two
The back nine. Use simulations to estimate more golf scores, similar to the procedure in Exercise 43.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 43.b) On a par 5, the second shot will reach the
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
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
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
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
Knees. Research reported in the spring of 2002 cast doubt on the effectiveness of arthroscopic knee surgery for patients with arthritis. Patients suffering from arthritis pain who volunteered to participate in the study were randomly divided into groups. One group received arthroscopic knee
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.
Save the grapes. Vineyard owners have problems with birds that like to eat the ripening grapes. Grapes damaged by birds cannot be used for winemaking (or much of anything else). Some vineyards use scarecrows to try to keep birds away. Others use netting that covers the plants. Owners really would
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 (The Weekly What makes you think these results are incomplete?d) The Pew researchers
Age and party. The Gallup Poll conducted a representative telephone survey during the first quarter of 1999.Among its reported results was the following table concerning the preferred political party affiliation of respondents and their ages:Standard, March 10, 1997). The Pew Research Foundation
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
Sex and violence. Does the content of a television program affect viewers memory of the products advertised in commercials? Design an experiment to compare the ability of viewers to recall brand names of items featured in commercials during programs with violent content, sexual content, or neutral
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
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
Youthful appearance. Readers Digest 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
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
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
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
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
Cloning. In September 1998, USA Weekend magazine asked, Should humans be cloned? Readers were invited to register a Yes or No answer by calling one of two different 900 numbers. Based on 38,023 responses, the magazine reported that 9 out of 10 readers oppose cloning.a) Explain why you think the
In another experiment to see if getting candy after a meal would induce customers to leave a bigger tip, a waitress randomly decided what to do with 80 dining parties. Some parties received no candy, some just one piece, and some two pieces. Others initially got just one piece of candy, and then
Tips, take
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
Cell phone risks. Researchers at the Washington University School of Medicine randomly placed 480 rats into one of three chambers containing radio antennas. One group was exposed to digital cell phone radio waves, the second to analog cell phone waves, and the third group to no radio waves. Two
Everyday randomness. Aside from casinos, lotteries, and games, there are other situations you encounter in which something is described as random in some way.Give three different examples. Describe how randomness is (or is not) achieved in each.
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
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
Point spread. When taking bets on sporting events, bookmakers often include a point spread that awards the weaker team extra points. In theory this makes the outcome of the bet a toss-up. Suppose a gambler places a$10 bet and picks the winners of five games. If he s right about fewer than three of
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
Physically fit people are less likely to die of cancer. A report in the May 2002 issue of Medicine and Science in Sports and Exercise followed 25,892 men aged 30 to 87 for 10 years. The most physically fit men had a 55% lower risk of death from cancer than the least fit group.
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
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 of those checked show signs of unsuitability for juice (bruised, rotten, unripe, etc.) the whole truckload is
Researchers at the University of Bristol (England) investigated reasons why different species of birds begin to sing at different times in the morning. They captured and examined birds of 57 species at seven different sites.They measured the diameter of the birds eyes and also recorded the time of
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
An artisan wants to create pottery that has the appearance of age. He prepares several samples of clay with four different glazes and test fires them in a kiln at three different temperature settings.
Researchers investigating appetite control as a means of losing weight found that female rats ate less and lost weight after injections of the hormone leptin, while male rats responded better to insulin. (Science News, July 20, 2002)
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
Can long-term exposure to strong electromagnetic fields cause cancer? Researchers in Italy tracked down 13 years of medical records for people living near Vatican Radio s powerful broadcast antennas. A disproportionate share of the leukemia cases occurred among men and children who lived within 6
Can makeup damage fetal development? Many cosmetics contain a class of chemicals called phthalates. Studies that exposed some laboratory animals to these chemicals found a heightened incidence of damage to male reproductive systems. Since traces of phthalates are found in the urine of women who use
Fireworks manufacturers face a dilemma. They must be sure that the rockets work properly, but test firing a rocket essentially destroys it. On the other hand, not testing the product leaves open the danger that they sell a bunch of duds, leading to unhappy customers and loss of future sales. The
In a study appearing in the journal Science, a research team reports 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
Almost 90,000 women participated in a 16-year study of the role of the vitamin folate in preventing colon cancer.Some of the women had family histories of colon cancer in close relatives. In this at-risk group, the incidence of colon cancer was cut in half among those who maintained a high folate
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
Researchers at the Purina Pet Institute studied Labrador retrievers for evidence of a relationship between diet and longevity. At 8 weeks of age, 2 puppies of the same sex and weight were randomly assigned to one of two groups a total of 48 dogs in all. One group was allowed to eat all they wanted,
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.
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. According to their report, published in the New England
Skydiving, anyone? A humor piece published in the British Medical Journal ( Parachute use to prevent death and major trauma related to gravitational challenge:systematic review of randomized control trials, Gordon, Smith, and Pell, BMJ, 2003:327) notes that we can t tell for sure whether parachutes
Washing clothes. A consumer group wants to test the effectiveness of a new organic laundry detergent and make recommendations to customers about how to best use the product. They intentionally get grass stains on 30 white T-shirts in order to see how well the detergent will clean them. They want to
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
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
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
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
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
Gas mileage. Do cars get better gas mileage with premium instead of regular unleaded gasoline? While it might be possible to test some engines in a laboratory setting, we d rather use real cars and real drivers in real day-to-day driving, so we get 20 volunteers. Design the experiment.
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.
Healing. A medical researcher suspects that giving postsurgical patients large doses of vitamin E will speed their recovery times by helping their incisions heal more quickly. Design an experiment to test this conjecture. Be sure to identify the factors, levels, treatments, response variable, and
Dowsing. A water dowser claims to be able to sense the presence of water using a forked stick. Suppose we wish to set up an experiment to test his ability. We get 20 identical containers, fill some with water, and ask the dowser to tell which ones are full and which empty.a) How will we randomize
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
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
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?
Frumpies. The makers of Frumpies, the breakfast of rug rats, want to improve their marketing, so they consult you:a) They first want to know what fraction of children, ages 10 to 13, like their celery-flavored cereal. What kind of study should they perform?b) They are thinking of introducing a new
More Mozart. The NY Times (Sept. 9, 1991) reported that A sake brewer [near] Tokyo is marketing a Mozart brand of sake, asserting that Mozart is regularly played at the brewery. It seems that the malt grows well especially with Mozart music in the background, the company director [said]. Suppose,
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
Diet and blood pressure. Exercise 12 reports on 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
Hamstrings. Exercise 25 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 14, 28, and 30 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, 27, and 29 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 14 and 28 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 27 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
Insomnia. Exercise 14 describes an experiment that showed that getting 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 37.4 days (SD = 27.6 days). Those assigned to a program of agility and trunk stabilization exercises returned to
Weight is an issue for both humans and their pets. 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
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
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
Scientists examined the glycogen content of rats brains at the rats normal bedtimes and after they had been kept awake for an extra 6, 12, or 24 hours. The scientists found that glycogen was 38% lower among rats that had been sleep-deprived for 12 hours or more, and that the levels recovered during
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 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
In 2001 a report in the Journal of the American Cancer Institute indicated that women who work nights have a 60% greater risk of developing breast cancer. Researchers based these findings on the work histories of 763 women with breast cancer and 741 women without the disease.
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.
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 industrial explosion and were under age 40 at the time. Fifteen of the women had developed breast cancer
Some gardeners prefer to use nonchemical methods to control insect pests in their gardens. Researchers have designed two kinds of traps and want to know which design will be more effective. They randomly choose 10 locations in a large garden and place one of each kind of trap at each location.
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
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
To research the effects of dietary patterns on blood pressure in 459 subjects, subjects were randomly assigned to three groups and had their meals prepared by dieticians.Those who were fed a diet low in fat and cholesterol and high in fruits, vegetables, and low-fat dairy foods (known as the DASH
An examination of the medical records of more than 360,000 Swedish men showed that those who were overweight or who had high blood pressure had a higher risk of kidney cancer. (New England Journal of Medicine 3434[2000]: 1305)
Among a group of disabled women aged 65 and older who were tracked for several years, those who had a vitamin B 12 deficiency were twice as likely to suffer severe depression as those who did not. (American Journal of Psychiatry 157 [2000]: 715)
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)
The leg muscles of men aged 60 to 75 were 50% to 80%stronger after they participated in a 16-week, highintensity resistance-training program twice a week.(Journal of Gerontology 55A [2000]: B336)
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?
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