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Stats Data And Models 3rd Canadian Edition Richard De Veaux, Paul Velleman, David Bock, Augustin Vukov, Augustine Wong - Solutions

Ottawa Seventy-six percent of Ottawans speak English only when they’re at home, 10% speak only French, 11%speak a non-official language, and the remainder speak more than one language. You are conducting a poll by calling Ottawans at random. In your first three calls, what is the probability you
The train 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 five-day work week, what is the probability that hea) Gets stopped on Monday and again
Champion bowler A certain bowler can bowl a strike 70% of the time. What is the probability that shea) 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 consecutive strikes)?
Slot machine A slot machine has three wheels that spin independently. Each has 10 equally likely symbols: four bars, three lemons, two cherries, and a bell. If you play, what is the probability thata) You get three lemons?b) You get no fruit symbols?c) You get three bells (the jackpot)?d) You get
Dice You roll a fair die three times. What is the probability thata) You roll all 6s?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 5s?
Disjoint or independent, again In Exercise 18, 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
Disjoint or independent? In Exercise 17, you calculated probabilities of getting various M&Ms. 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
Blood Canadian Blood Services says that about 46% of the Canadian population have Type O blood, 42% have Type A, 9% have Type B, and the rest have Type AB. Among four potential donors, what is the probability thata) All are Type O?b) No one is Type AB?c) They are not all Type A?d) At least one
M&Ms The Masterfoods company says that before the introduction of purple, yellow candies made up 20% of their plain M&Ms; red another 20%; and orange, blue, and green each made up 10%. The rest were brown. If you pick three M&Ms in a row, what is the probability thata) They are all brown?b) The
Optimistic A Nanos Poll in November 2008 asked 1000 Canadian adults to compare Canada’s international reputation in 2008 with its international reputation in 2007. Here’s how they responded:Response Number Not improved 251 No change 313 Somewhat improved 288 Improved 120 No opinion 28 Total
Ethanol A Nanos Poll in August 2008 asked 500 adult Ontarians if they thought Ontario should produce more, produce less, or maintain current production of ethanol. Ethanol is made from corn, and can be used as a gasoline additive to increase fuel efficiency. Here’s how they responded:Response
Online banking again Suppose that the information in Exercise 8 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
Facebook again Suppose that the information in Exercise 9 had been presented in the following way. Facebook reports that 86% of its users are from outside of North America. Of the North American users, twothirds log on every day. Of the non-North American users, three-sevenths log on every day.
Online banking 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?
Facebook Facebook reports that 86% of its users are from outside of North America and that 46.2% of its users log on to Facebook every day. Suppose that 9.3% of its users are North American users who log on every day. Make a probability table. Why is a table better than a tree here?
Field goals A nervous kicker usually makes 70% of his first field goal attempts. If he makes his first attempt, his success rate rises to 90%. What is the probability that he makes his first two kicks?
Late to the bus A student figures that he has a 30% chance of being let out of class late. If he leaves class late, there is a 45% chance that he will miss his bus. What is the probability that he is let out of class late and misses the bus?
Sports again From Exercise 1, if someone doesn’t like to watch basketball, what is the probability that she will be a hockey fan? Hockey No Hockey Basketball 27 13 No Basketball 38 22
Sports What is the probability that a person likes to watch hockey, given that she also likes to watch basketball?
Simulations again Suppose two hockey teams are equally matched, and play a series of 10 games. Use simulations to estimate the probability that at least one of the two teams will have a win streak of at least four games at some time in the series. Use software to draw randomly from the digits 0
Simulations Probabilities at times can be hard to determine mathematically. By building a simulation to model the trials, we can estimate probabilities using computer power instead. Use simulations to estimate the probability that at least two people have the same birthday in a random group of 40
Lottery Lilith never selects 1, 2, 3, 4, 5, and 6 when she gets a Lotto 6/49 ticket. After all, everyone knows this will never win. Next time she buys a ticket, however, she selects 4, 9, 14, 22, 36, and 41, believing her choices are better than 1, 2, 3, 4, 5, and 6.Is Lilith’s reasoning
Poker A poker hand consists of five cards. You are dealt all four aces and the king of spades. Your buddy is dealt 10 1, 9 0, 7 3, 4 2, 2 1.Does your hand have a smaller probability than your buddy’s? Explain.
Gambling The game of Craps starts with a player tossing a pair of dice. If the dice add up to 2 or 3 or 12, the player’s turn is up and they “crap out.” What is the probability of crapping out?
Birth order 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:Birth Order 1 or only 2 or more Total Arts & Sciences 34 23 57 Agriculture 52 41 93 Human
Cosmetic marketing A GfK Roper Worldwide survey asked consumers in five countries whether they agreed with the statement “I follow a skin care routine every day.” Here are the responses classified by the country of the respondent.Country Agree Disagree Don’t Know Total China 361 988 153 1502
Workers Employment data at a large company reveal that 72% of the workers are married, 44% are university graduates, and half of the university graduates are married. What is the probability that a randomly chosen workera) Is neither married nor a university graduate?b) Is married but not a
Emigration In 2007, 51% of all emigrants from Canada were males, 82% were at least 18 years old, and 42% were males of at least 18 years of age. Find the probability that a randomly selected person who emigrated from Canada in 2007 wasa) Male and under 18 years old.b) Either male or at least 18
Immigration In 2014, 52.3% of all immigrants to Canada were females, 18.6% were under 18 years old, and 9.0% were females under 18 years old. Find the probability that a randomly selected person who immigrated to Canada in 2014 wasa) Female and at least 18 years old.b) Either female or under 18
Homes Real estate ads suggest that 64% of homes for sale have garages, 21% have swimming pools, and 17% have both features. What is the probability that a home for sale hasa) A pool or a garage?b) Neither a pool nor a garage?c) A pool but no garage?
Census Canada conducts a census every five years. Federal, provincial, and local governments use census data to shape public policy. In 2006, Canada tried something no other country had ever tried—census questionnaires that could be completed online. Sixty-six percent of households completed
Optimism A Nanos Poll conducted in May 2012 asked 1000 Canadians whether they think the next generation will have a standard of living that is higher, the same, or lower than what Canadians have today. Here’s how they responded:If we select a person at random from this sample of 1000 adults,a)
Ethanol A Nanos Poll in August 2008 asked 500 adult Ontarians if they thought Ontario should produce more, produce less, or maintain current production of ethanol. Ethanol is made from corn, and can be used as a gasoline additive to increase fuel efficiency. Here’s how they responded:If we select
Stats projects 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
Car repairs A consumer organization estimates that over a one-year period, 17% of cars will need to be repaired once, 7% will need repairs twice, and 4% will require three or more repairs. What is the probability that a car chosen at random will needa) No repairs?b) No more than one repair?c) Some
Scratch off 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 totalled at the cash register. The store is required to reveal (in
Spinner The plastic arrow on a spinner for a child’s game stops rotating to point at a colour that will determine what happens next. Which of the following probability assignments are possible? Probabilities of... Red Yellow Green Blue a) 0.25 0.25 0.25 0.25 b) 0.10 0.20 0.30 0.40 c) 0.20 0.30
Jackpot 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
Fire insurance Insurance companies collect annual payments from homeowners in exchange for paying to rebuild houses that burn down.a) Why should you be reluctant to accept a $300 payment from your neighbour to replace his house should it burn down during the coming year?b) Why can the insurance
Crash 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
Cold streak A batter who failed to get a hit in seven consecutive times at bat hits a game-winning home run. When speaking with reporters after the game, he says he was very confident on his last time up at bat because he knew he was “due for a hit.” Comment on the batter’s reasoning.
Snow 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.
Winter 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
Rain The weather reporter on television makes predictions such as a 25% chance of rain. What do you think such a phrase means?
Sample spaces II 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 three children; record each child’s gender in order of birth.c) Toss four coins; record the number of tails.d)
Sample spaces For each of the following, list the sample space and tell whether you think the events are equally likely.a) Toss two coins; record the order of heads and tails.b) A family has three children; record the number of boys.c) Flip a coin until you get a head or three consecutive tails;
Cooking and shopping 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?
Pet ownership 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?
Playlist II In Exercise 6, your list of favorite songs includes 10 rock songs, 7 rap songs and 3 country songs. What is the probability that a randomly played song is either a rap song or a country song?
Wardrobe II In Exercise 5, you have five blue shirts, three red shirts and two black shirts in your dresser. What is the probability that a randomly selected shirt is either a blue or a black shirt?
Playlists Your list of favourite 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 Rolling a fair six-sided die is supposed to randomly generate the numbers 1 through 6.Explain what random means in this context.
Security Twenty first-class passengers and 120 coach passengers are 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
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
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 Standard, March 10, 1997). The Pew Research Foundation tested this
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
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
Age and party 2008 The Pew Research Center collected data from national exits polls conducted by NBC News after the 2008 U.S. presidential election. The following table shows information regarding voter age and party preference: Age Republican Democrat Other Total 18–29 260 390 351 1001 30–44
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
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 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 university Statistics class conducted a survey concerning community attitudes about the school’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
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 will stain 16 swatches of cloth with 2 tsp of a
Timing A Léger Marketing online poll conducted in June of 2013 showed Justin Trudeau of the Liberal party with a four-point lead over current Prime Minister Stephen Harper. Considering the survey design, can you think of any reasons why Stephen Harper might still win the election, were it to be
Tips, second course 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
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
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 soft drinks 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
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
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 U.S. states who answered questions about their health, smoking history, alcohol intake, diet,
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 seem 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,
People who read the last page of a mystery novel first generally like stories better. Researchers recruited 819 college students to read short stories. 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 a study appearing 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
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. The study concluded that those receiving the folic acid may actually increase their risk of developing
The radioactive gas radon, found in some homes, poses a health risk to residents. To assess the level of contamination in their area, a municipal 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
Researchers at the Purina Pet Institute studied Labrador retrievers for evidence of a relationship between diet and longevity. At eight weeks of age, 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 three 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 humour piece published in the British Medical Journal notes that we can’t tell for sure whether parachutes are safe and effective because there has never been a properly randomized, double-blind, placebo-controlled study of parachute effectiveness in skydiving.26 (Yes, this
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 to see how well the detergent will clean them. They want to try
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.
LSAT prep Can test prep courses actually help raise LSAT scores? One organization says that the 30 students they tutored achieved an average gain of 15 points when they retook the test.a) Explain why this does not necessarily prove that the test prep 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
Weekend deaths A study published in the New England Journal of Medicine (August 2001)25 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? 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.
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 ones are empty.a) How will we
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

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