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intro stats
Intro Stats 4th International Edition Richard D. De Veaux, Paul F. Velleman, David Bock - Solutions
Cell phones and surveys A 2010 study conducted by the National Center for Health Statistics found that 25% of U.S. households had no landline service. This raises concerns about the accuracy of certain surveys, as they depend on random-digit dialing to households via landlines. We are going to pick
Playlists Your list of favorite songs contains 10 rock songs, 7 rap songs, and 3 country songs.a) What is the probability that a randomly played song is a rap song?b) What is the probability that a randomly played song is not country?
Wardrobe In your dresser are five blue shirts, three red shirts, and two black shirts.a) What is the probability of randomly selecting a red shirt?b) What is the probability that a randomly selected shirt is not black?
Dice II After rolling doubles on a pair of dice three times in a row, your friend exclaims, “I can’t get doubles four times in a row!” Explain why this thinking is incorrect.
Flipping a coin II Your friend says: “I flipped five heads in a row! The next one has to be tails!” Explain why this thinking is incorrect.
Explain what random means in this context.
Dice Rolling a fair six-sided die is supposed to randomly generate the numbers 1 through
Flipping a coin Flipping a fair coin is said to randomly generate heads and tails with equal probability. Explain what random means in this context.
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 think?
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
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
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. 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
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
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
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
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
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
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
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
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
Tips, take 2 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
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 years
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.
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
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
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
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
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 show signs of unsuitability for juice (bruised, rotten, unripe, etc.), the whole truckload is rejected.
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
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.
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
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
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
People who read the last page of a mystery novel first generally like stories better. Researchers recruited 819 college students to read short stories, and for one story, they were given a spoiler paragraph beforehand. On the second and third story, the spoiler was incorporated as the opening
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 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
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
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
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. Their report, published in the New England Journal of
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
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 stain 30 white T-shirts with grass in order to see how well the detergent will clean them. They want
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
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.
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 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
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
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.
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 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 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
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 2012 Summer Olympic games. To test the shoe, it has all 5 runners run the 100-meter dash with a competitor’s shoe
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.
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?
Insomnia, at last Exercises 24, 36, and 38 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
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
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
Insomnia Exercise 24 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 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
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. (Source: 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
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 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.
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)
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 diet;
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)
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)
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)
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 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
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
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