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Stats Data And Models 4th Edition Richard D. De Veaux, Paul D. Velleman, David E. Bock - Solutions

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
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
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. Read each brief
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
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
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
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
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. Read each brief report
Pew Research compared respondents to an ordinary 5-day telephone survey with respondents to a 4-month-long 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
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
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
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?
Describe a strategy to randomly split 24 tomato plants into the three groups for the completely randomized single factor experiment of Exercise 4.
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
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
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
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
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
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.
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
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
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
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 the role
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.
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.
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
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
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
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 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
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 to try the detergent
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 are safe and
For the experiment of Exercise 3, name some variables the driver did or should have controlled. Was the experiment randomized and replicated? Exercise 3 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
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 You want to compare the tastiness and juiciness of tomatoes grown with three amounts of a new fertilizer: none, half the recommended
Is the experiment of Exercise 3 blinded? Can it be double-blinded? Explain. Exercise 3 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
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 coin 10 times;
A casino claims that its roulette wheel is truly random. What should that claim mean?
Comment on the following quotation: "What I think is our best determination is it will be a colder than normal winter'' said Pamela Naber Knox, a Wisconsin state climatologist. "I'm basing that on a couple of different things. First, in looking at the past few winters, there has been a lack of
After an unusually dry autumn, a radio announcer is heard to say, "Watch out! We'll pay for these sunny days later on this winter." Explain what he's trying to say, and comment on the validity of his reasoning.
A basketball player missed 8 of 11 shots in the final portion of a game. When talking to reporters afterward, he says that he's not worried about his next game because he's due to make a lot of shots. Comment on his reasoning.
Commercial airplanes have an excellent safety record. Nevertheless, there are crashes occasionally, with the loss of many lives. In the weeks following a crash, airlines often report a drop in the number of passengers, probably because people are afraid to risk flying. a) A travel agent suggests
Insurance companies collect annual payments from drivers in exchange for paying for the cost of accidents.a) Why should you be reluctant to accept a $ 1500 payment from your neighbor to cover his automobile accidents in the next year?b) Why can the insurance company make that offer?
On February 11, 2009, the AP news wire released the following story:(LAS VEGAS, Nev.)—A man in town to watch the NCAA basketball tournament hit a $38.7 million jackpot on Friday, the biggest slot machine payout ever. The 25-year-old software engineer from Los Angeles, whose name was not released
The plastic arrow on a spinner for a child's game stops rotating to point at a color that will determine what happens next. Which of the following probability assignments are legitimate?
Many stores run "secret sales": Shoppers receive cards that determine how large a discount they get, but the percentage is revealed by scratching off that black stuff (what is that?) only after the purchase has been totaled at the cash register. The store is required to reveal (in the fine print)
Traffic checks on a certain section of highway suggest that 60% of drivers are speeding there. Since 0.6 × 0.6 = 0.36, the Multiplication Rule might suggest that there's a 36% chance that two vehicles in a row are both speeding. What's wrong with that reasoning?
For high school students graduating in 2013, college admissions to the nation's most selective schools were the most competitive in memory. Harvard accepted about 5.8% of its applicants, Dartmouth 10%, and Penn 12.1%. Jorge has applied to all three. Assuming that he's a typical applicant, he
In Exercise 25, we saw that in 2013 Harvard accepted about 5.8% of its applicants, Dartmouth 10%, and Penn 12.1%. Jorge has applied to all three. He figures that his chances of getting into at least one of the three must be about 27.9%. a) How has he arrived at this conclusion? b) What assumption
A consumer organization estimates that over a 1-year period 17% of cars will need to be repaired only once, 7% will need repairs exactly twice, and 4% will require three or more repairs. What is the probability that a car chosen at random will need a) No repairs? b) No more than one repair? c) Some
In a large Introductory Statistics lecture hall, the professor reports that 55% of the students enrolled have never taken a Calculus course, 32% have taken only one semester of Calculus, and the rest have taken two or more semesters of Calculus. The professor randomly assigns students to groups of
Consider again the auto repair rates described in Exercise 27. If you own two cars, what is the probability that a) Neither will need repair? b) Both will need repair? c) At least one car will need repair? Exercise 27 A consumer organization estimates that over a 1-year period 17% of cars will need
You are assigned to be part of a group of three students from the Intro Stats class described in Exercise 28. What is the probability that of your other two groupmates, a) Neither has studied Calculus? b) Both have studied at least one semester of Calculus? c) At least one has had more than one
You used the Multiplication Rule to calculate repair probabilities for your cars in Exercise 29. a) What must be true about your cars in order to make that approach valid? b) Do you think this assumption is reasonable? Explain.
A Gallup Poll (www.gallup.com/poll/161729/americans-divided-energy-environment-trade-off.aspx) in March 2013 asked 529 U.S. adults whether increasing oil, gas, and coal production or developing alternative energy sources such as wind and solar power should be given a higher priority. Here are the
A Pew Research poll in 2011 asked 2005 U.S. adults whether being a father today is harder than it was a generation ago. Here's how they responded:Response NumberEasier …………………… 501Same …………………… 802Harder…………………… 682No Opinion
Exercise 33 shows the results of a Gallup Poll about energy. Suppose we select three people at random from this sample. Response Number Oil, gas, coal …………….. 164 Wind and solar ………….. 312 Equally Important ……….. 37 No Opinion ……………… 16 Total
Consider again the results of the poll about fathering discussed in Exercise 34. If we select two people at random from this sample, Response Number Easier …………………… 501 Same …………………… 802 Harder …………………… 682 No Opinion ………………
As mentioned in the chapter, opinion-polling organizations contact their respondents by sampling random telephone numbers. Although interviewers can reach about 62% of U.S. households, the percentage of those contacted who agree to cooperate with the survey fell from 43% in 1997 to 14% in 2012.
According to Pew Research, the contact rate (probability of contacting a selected household) was 90% in 1997 and 62% in 2012. However, the cooperation rate (probability of someone at the contacted household agreeing to be interviewed) was 43% in 1997 and dropped to 14% in 2012.a) What is the
The Mars company says that before the introduction of purple, yellow candies made up 20% of their plain M&M's, red another 20%, and orange, blue, and green each made up 10%. The rest were brown.a) If you pick an M&M at random, what is the probability that1. It is brown?2. It is yellow or
The American Red Cross says that about 45% of the U.S. population has Type O blood, 40% Type A, 11% Type B, and the rest Type AB. a) Someone volunteers to give blood. What is the probability that this donor 1. Has Type AB blood? 2. Has Type A or Type B? 3. Is not Type O? b) Among four potential
In Exercise 39, you calculated probabilities of getting various M&M's. Some of your answers depended on the assumption that the outcomes described were disjoint; that is, they could not both happen at the same time. Other answers depended on the assumption that the events were independent; that
In Exercise 40, you calculated probabilities involving various blood types. Some of your answers depended on the assumption that the outcomes described were disjoint; that is, they could not both happen at the same time. Other answers depended on the assumption that the events were independent;
You roll a fair die three times. What is the probability that a) You roll all 6's? b) You roll all odd numbers? c) None of your rolls gets a number divisible by 3? d) You roll at least one 5? e) The numbers you roll are not all 5's?
A slot machine has three wheels that spin independently. Each has 10 equally likely symbols: 4 bars, 3 lemons, 2 cherries, and a bell. If you play, what is the probability that a) You get 3 lemons? b) You get no fruit symbols? c) You get 3 bells (the jackpot)? d) You get no bells? e) You get at
A certain bowler can bowl a strike 70% of the time. If the bowls are independent, what's the probability that she a) Goes three consecutive frames without a strike? b) Makes her first strike in the third frame? c) Has at least one strike in the first three frames? d) Bowls a perfect game (12
To get to work, a commuter must cross train tracks. The time the train arrives varies slightly from day to day, but the commuter estimates he'll get stopped on about 15% of work days. During a certain 5-day work week, what is the probability that he a) Gets stopped on Monday and again on
Suppose that in your city 37% of the voters are registered as Democrats, 29% as Republicans, and 11 % as members of other parties (Liberal, Right to Life, Green, etc.). Voters not aligned with any official party are termed "Independent." You are conducting a poll by calling registered voters at
Census reports for a city indicate that 62% of residents classify themselves as Christian, 12% as Jewish, and 16% as members of other religions (Muslims, Buddhists, etc.). The remaining residents classify themselves as nonreligious. A polling organization seeking information about public opinions
You purchased a five-pack of new light bulbs that were recalled because 6% of the lights did not work. What is the probability that at least one of your lights is defective?
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?
For a sales promotion, the manufacturer places winning symbols under the caps of 10% of all Pepsi bottles. You buy a six-pack. What is the probability that you win something?
On September 11, 2002, the first anniversary of the terrorist attack on the World Trade Center, the New York State Lottery's daily number came up 9-1-1. An interesting coincidence or a cosmic sign?a) What is the probability that the winning three numbers match the date on any given day?b) What is
You shuffle a deck of cards and then start turning them over one at a time. The first one is red. So is the second. And the third. In fact, you are surprised to get 10 red cards in a row. You start thinking, "The next one is due to be black!" a) Are you correct in thinking that there's a higher
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?
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 five U.S. households at
The survey by the National Center for Health Statistics further found that 49% of adults ages 25-29 had only a cell phone and no landline. We randomly select four 25-29-year-olds:a) What is the probability that all of these adults have a only a cell phone and no landline?b) What is the probability
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; record each flip.d) Roll
Suppose that 25% of people have a dog, 29% of people have a cat, and 12% of people own both. What is the probability that someone owns a dog or a cat?
A national survey indicated that 30% of adults conduct their banking online. It also found that 40% are younger than 50, and that 25% are younger than 50 and conduct their banking online. Make a probability table. Why is a table better than a tree here?
Suppose that the information in Exercise 9 had been presented in the following way. Facebook reports that 70% of its users are from outside the United States. Of the U.S. users, two-thirds log on every day. Of the non-U.S. users, three-sevenths log on every day. Draw a tree for this situation. Why
Suppose that the information in Exercise 10 had been presented in the following way. A national survey of bank customers finds that 40% are younger than 50. Of those younger than 50, 5 of 8 conduct their banking online. Of those older than 50, only 1 of 12 banks online. Draw a tree for this
Given the probabilities in Exercise 11, what is the probability that a person is from the United States given that he logs on to Facebook every day? Has the probability that he is from the United States increased or decreased with the additional information? In Exercise 11 Suppose that the
Given the probabilities in Exercise 12, what is the probability that a person is younger than 50 given that she uses online banking? Has the probability that she is younger than 50 increased or decreased with the additional information?In Exercise 12Suppose that the information in Exercise 10 had
Recent research suggests that 73% of Americans have a home phone, 83% have a cell phone, and 58% of people have both. What is the probability that an American hasa) A home or cell phone?b) Neither a home phone nor a cell phone?c) A cell phone but no home phone?
Suppose the probability that a U.S. resident has traveled to Canada is 0.18, to Mexico is 0.09, and to both countries is 0.04. What's the probability that an American chosen at random hasa) Traveled to Canada but not Mexico?b) Traveled to either Canada or Mexico?c) Not traveled to either country?
A check of dorm rooms on a large college campus revealed that 38% had refrigerators, 52% had TVs, and 21% had both a TV and a refrigerator. What's the probability that a randomly selected dorm room has a) A TV but no refrigerator? b) A TV or a refrigerator, but not both? c) Neither a TV nor a
Employment data at a large company reveal that 72% of the workers are married, that 44% are college graduates, and that half of the college grads are married. What's the probability that a randomly chosen worker a) Is neither married nor a college graduate? b) Is married but not a college
The marketing research organization GfK Roper conducts a yearly survey on consumer attitudes worldwide. They collect demographic information on the roughly 1500 respondents from each country that they survey. Here is a table showing the number of people with various levels of education in five
Forty-five percent of Americans like to cook and 59% of Americans like to shop, while 23% enjoy both activities. What is the probability that a randomly selected American either enjoys cooking or shopping or both?
A survey of students in a large Introductory Statistics class asked about their birth order (1 = oldest or only child) and which college of the university they were enrolled in. Here are the data:Suppose we select a student at random from this class. What is the probability that the person isa) A
You draw a card at random from a standard deck of 52 cards. Find each of the following conditional probabilities: a) The card is a heart, given that it is red. b) The card is red, given that it is a heart. c) The card is an ace, given that it is red. d) The card is a queen, given that it is a face
In its monthly report, the local animal shelter states that it currently has 24 dogs and 18 cats available for adoption. Eight of the dogs and 6 of the cats are male. Find each of the following conditional probabilities if an animal is selected at random:a) The pet is male, given that it is a
The probabilities that an adult American man has high blood pressure and/or high cholesterol are shown in the table.What's the probability thata) A man has both conditions?b) A man has high blood pressure?c) A man with high blood pressure has high cholesterol?d) A man has high blood pressure if
The table shows the political affiliations of U.S. voters and their positions on supporting stronger immigration enforcement.a) What's the probability thati) A randomly chosen voter favors stronger immigration enforcement?ii) A Republican favors stronger enforcement?iii) A voter who favors stronger
Look again at the table summarizing the Roper survey in Exercise 19.a) If we select a respondent at random, what's the probability we choose a person from the United States who has done post-graduate study? b) Among the respondents who have done post-graduate study, what's the probability the
Look again at the data about birth order of Intro Stats students and their choices of colleges shown in Exercise 20.a) If we select a student at random, what's the probability the person is an Arts and Sciences student who is a second child (or more)? b) Among the Arts and Sciences students, what's
Seventy percent of kids who visit a doctor have a fever, and 30% of kids with a fever also have sore throats. What's the probability that a kid who goes to the doctor has a fever and a sore throat?

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