Stats Data And Models 5th Edition Richard D De Veaux, Paul F Velleman, David E Bock - Solutions

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
Internet speed Carsten, Matt, and Rainer designed an experiment to see how different environments affect the Internet speed around campus. They used their own Mac computer and a PC belonging to the school and tested each in two different libraries, the main and the science library. Other factors
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.
Dice Rolling a fair six-sided die is supposed to randomly generate the numbers 1 through 6. Explain what random means in this context.
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.
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.
Electronics Suppose that 46% of families living in a certain county own a computer and 18% own an HDTV. The Addition Rule might suggest, then, that 64% of families own either a computer or an HDTV. What’s wrong with that reasoning?
Homes Funding for many schools comes from taxes based on assessed values of local properties. People’s homes are assessed higher if they have extra features such as garages and swimming pools. Assessment records in a certain school district indicate that 37% of the homes have garages and 3% have
Lefties Although it’s hard to be definitive in classifying people as right- or left-handed, some studies suggest that about 14% of people are left-handed. Since 0.14 × 0.14 = 0.0196, the Multiplication Rule might suggest that there’s about a 2% chance that a brother and a sister are both
Quality control A consumer organization estimates that 29% of new cars have a cosmetic defect, such as a scratch or a dent, when they are delivered to car dealers. This same organization believes that 7% have a functional defect—something that does not work properly—and that 2% of new cars have
Workers A company’s human resources officer reports a breakdown of employees by job type and sex shown in the table.1. What’s the probability that a worker selected at random isi). Female?ii). Female or a production worker?iii). Female, if the person works in production?iv). A production
Toasters A manufacturer ships toasters in cartons of 20. In each carton, they estimate a 5% chance that one of the toasters will need to be sent back for minor repairs. What is the probability that in a carton, there will be exactly 3 toasters that need repair?
Airfares Each year a company must send 3 officials to a meeting in China and 5 officials to a meeting in France. Airline ticket prices vary from time to time, but the company purchases all tickets for a country at the same price. Past experience has shown that tickets to China have a mean price of
Soccer A soccer team estimates that they will score on 8% of the corner kicks. In next week’s game, the team hopes to kick 15 corner kicks. What are the chances that they will score on 2 of those opportunities?
Bipolar Psychiatrists estimate that about 1 in 100 adults suffers from bipolar disorder. What’s the probability that in a city of 10,000 there are more than 200 people with this condition? Be sure to verify that a Normal model can be used here.
A game To play a game, you must pay $5 for each play. There is a 10% chance you will win $5, a 40% chance you will win $7, and a 50% chance you will win only $3.1. What are the mean and standard deviation of your net winnings?2. You play twice. Assuming the plays are independent events, what are
Soccer again If this team has 200 corner kicks over the season, what are the chances that they score more than 22 times?
Emergency switch Safety engineers must determine whether industrial workers can operate a machine’s emergency shutoff device. Among a group of test subjects, 66% were successful with their left hands, 82% with their right hands, and 51% with both hands.1. What percent of these workers could not
Twins In the United States, the probability of having twins (usually about 1 in 90 births) rises to about 1 in 10 for women who have been taking the fertility drug Clomid. Among a group of 10 pregnant women, what’s the probability that1. At least one will have twins if none were taking a
Deductible A car owner may buy insurance that will pay the full price of repairing the car after an at-fault accident, or save $12 a year by getting a policy with a $500 deductible. Her insurance company says that about 0.5% of drivers in her area have an at-fault auto accident during any given
Simulating the model Think about the Hope Solo picture search again. You are opening boxes of cereal one at a time looking for her picture, which is in 20% of the boxes. You want to know how many boxes you might have to open in order to find Hope.1. Describe how you would simulate the search for
Simulation II You are one space short of winning a child’s board game and must roll a 1 on a die to claim victory. You want to know how many rolls it might take.1. Describe how you would simulate rolling the die until you get a 1.2. Run at least 30 trials.3. Based on your simulation, estimate the
Hope, again Let’s take one last look at the Hope Solo picture search. You know her picture is in 20% of the cereal boxes. You buy five boxes to see how many pictures of Hope you might get.1. Describe how you would simulate the number of pictures of Hope you might find in five boxes of cereal.2.
Seatbelts Suppose 75% of all drivers always wear their seatbelts. Let’s investigate how many of the drivers might be belted among five cars waiting at a traffic light.1. Describe how you would simulate the number of seatbelt-wearing drivers among the five cars.2. Run at least 30 trials.3. Based
Stocks Since the stock market began in 1872, stock prices have risen in about 73% of the years. Assuming that market performance is independent from year to year, what’s the probability that1. The market will rise for 3 consecutive years?2. The market will rise 3 years out of the next 5?3. The
On time A Department of Transportation report about air travel found that, nationwide, 76% of all flights are on time. Suppose you are at the airport and your flight is one of 50 scheduled to take off in the next two hours. Can you consider these departures to be Bernoulli trials? Explain.
Multiple choice A multiple choice test has 50 questions, with 4 answer choices each. You must get at least 30 correct to pass the test, and the questions are very difficult.1. Are you likely to be able to pass by guessing on every question? Explain.2. Suppose, after studying for a while, you
Lost luggage A Department of Transportation report about air travel found that airlines misplace about 5 bags per 1000 passengers. Suppose you are traveling with a group of people who have checked 22 pieces of luggage on your flight. Can you consider the fate of these bags to be Bernoulli trials?
Stock strategy Many investment advisors argue that after stocks have declined in value for 2 consecutive years, people should invest heavily because the market rarely declines 3 years in a row.1. Since the stock market began in 1872, there have been two consecutive losing years eight times. In six
Hoops A basketball player has made 80% of his foul shots during the season. Assuming the shots are independent, find the probability that in tonight’s game he1. Misses for the first time on his fifth attempt.2. Makes his first basket on his fourth shot.3. Makes his first basket on one of his
Teen smoking II Suppose that, as reported by the Centers for Disease Control, about 18% of high school students smoke tobacco. You randomly select 120 high school students to survey them on their attitudes toward scenes of smoking in the movies.1. What’s the expected number of smokers?2. What’s
Youth survey According to a recent Gallup survey, 93% of teens use the Internet, but there are differences in how teen boys and girls say they use computers. The telephone poll found that 77% of boys had played computer games in the past week, compared with 65% of girls. On the other hand, 76% of
Insurance A 65-year-old woman takes out a $100,000 term life insurance policy. The company charges an annual premium of $520. Estimate the company’s expected profit on such policies if mortality tables indicate that only 2.6% of women age 65 die within a year.
Teen smoking The Centers for Disease Control and Prevention say that about 18% of high-school students smoke tobacco (down from a high of 38% in 1997). Suppose you randomly select high-school students to survey them on their attitudes toward scenes of smoking in the movies. What’s the probability
Dropouts One study comparing various treatments for the eating disorder anorexia nervosa initially enlisted 198 subjects, but found overall that 105 failed to complete their assigned treatment programs. Construct and interpret an appropriate confidence interval. Discuss any reservations you have
Babies The National Perinatal Statistics Unit of the Sydney Children’s Hospital reports that the mean birth weight of all babies born in birth centers in Australia in a recent year was 3564 grams—about 7.86 pounds. A Missouri hospital reports that the average weight of 112 babies born there
Hurricanes, redux We have looked at various facts about hurricanes in previous chapters. Suppose we find that the arrivals of hurricanes can be modeled by a Poisson distribution with mean 2.45.1. What’s the probability of no hurricanes next year?2. What’s the probability that during the next
Socks In your sock drawer you have 4 blue socks, 5 gray socks, and 3 black ones. Half asleep one morning, you grab 2 socks at random and put them on. Find the probability you end up wearing1. 2 blue socks.2. No gray socks.3. At least 1 black sock.4. A green sock.5. Matching sock
Volcanoes Almost every year, there is some incidence of volcanic activity on the island of Japan. In 2005 there were 5 volcanic episodes, defined as either eruptions or sizable seismic activity. Suppose the mean number of episodes is 2.4 per year. Let X be the number of episodes in the 2-year
Who’s the boss? The 2013 State of Women-Owned Businesses Report commissioned by American Express (www.womenable.com/content/userfiles/2013_State_of_Women-Owned_Businesses_Report_FINAL.pdf) says that, excluding large, publicly traded firms, women-owned firms make up 30% of the privately held firm
Meals A college student on a seven-day meal plan reports that the amount of money he spends daily on food varies with a mean of $13.50 and a standard deviation of $7.1. What are the mean and standard deviation of the amount he might spend in two consecutive days?2. What assumption did you make in
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
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
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
A&M again The president of the university plans a speech to an alumni group. He plans to talk about the proportion of students who responded in the survey that they are the first in their family to attend college, but the first draft of his speech treats that proportion as the actual proportion
Happy employees The company plans to have the head of each corporate division hold a meeting of their employees to ask whether they are happy on their jobs. They will ask people to raise their hands to indicate whether they are happy. What problems do you see with this plan?
French Consider the association between a student’s score on a French vocabulary test and the weight of the student. What direction and strength of correlation would you expect in each of the following situations? Explain.1. The students are all in third grade.2. The students are in third through
Winter in the city Summary statistics for the data relating the Latitude and average January temperature for 55 large U.S. cities are given below.1. What percent of the variation in January Temperature can be explained by variation in Latitude?2. What is indicated by the fact that the correlation
Smoking and pregnancy 2011 The Child Trends Data Bank monitors issues related to children. The table shows a 50-state average of the percent of expectant mothers who smoked cigarettes during their pregnancies.1. Create a scatterplot and describe the trend you see.2. Find the correlation.3. How is
How old is that tree? One can determine how old a tree is by counting its rings, but that requires either cutting the tree down or extracting a sample from the tree’s core. Can we estimate the tree’s age simply from its diameter? A forester measured 27 trees of the same species that had been
Colorblind Although some women are colorblind, this condition is found primarily in men. Why is it wrong to say there’s a strong correlation between Sex and Colorblindness?
Cars, fuel efficiency Consider a regression to predict the fuel efficiency (as miles per gallon, MPG) of the cars in the Cars data file. Here is one regression model using the Weight and the Drive Ratio:Response variable is: MPGR-squared = 89.5% s = 2.1861. What is the interpretation
Cars, correlations What factor most explains differences in Fuel Efficiency among cars? Below is a correlation matrix exploring that relationship for the car’s Weight (1000 lb), Horsepower, Displacement, and number of Cylinders. (Data in Cars)1. Which factor seems most strongly associated with
More indicators For each of these potential predictor variables say whether they should be represented in a regression model by indicator variables. If so, then suggest what specific indicators should be used (that is, what values they would have).a. In a regression to predict income, the age of
Approval 2016 President Obama was very popular at the end of his eight years in office. A CNN/ORC poll of 1000 U.S. adults conducted in the week before the end of his term found that 63% of Americans said they held a favorable view of the President
Bimodal We are sampling randomly from a distribution known to be bimodal.1. As our sample size increases, what’s the expected shape of the sample’s distribution?2. What’s the expected value of our sample’s mean? Does the size of the sample matter?3. How is the variability of sample means
Polling 2016 The 2016 U.S. presidential election was unusual in several ways. First, the candidate who won the most electoral votes, Donald Trump, did not win the most popular votes. Second, several minor-party candidates received enough votes to possibly affect the outcome. The official results
Scrabble Using a computer to play many simulated games of Scrabble, researcher Charles Robinove found that the letter “A” occurred in 54% of the hands. This study had a margin of error of ±10% (Chance, 15, no. 1 [2002])1. Explain what the margin of error means in this context.2. Why might the
Archery A champion archer can generally hit the bull’s-eye 80% of the time. Suppose she shoots 200 arrows during competition. Let p^ represent the percentage of bull’s-eyes she gets (the sample proportion).1. What are the mean and standard deviation of the sampling distribution model for p^?2.
Color-blind Medical literature says that about 8% of males are color-blind. A university’s introductory psychology course is taught in a large lecture hall. Among the students, there are 325 males. Each semester when the professor discusses visual perception, he shows the class a test for color
Fake news In a survey of 1002 U.S. adults in December 2016 by Pew Research (www.journalism.org/2016/12/15/many-americans-believe-fake-news-is-sowing-confusion/), 64% of adult respondents say they think that made-up “news” is causing a great deal of confusion about the basic facts of current
Gay marriage In June 2017, Pew Research asked a random sample of 2504 U.S. adults, “Do you strongly favor, favor, oppose, or strongly oppose allowing gays and lesbians to marry legally?”
Who’s the boss? The 2016 State of Women-Owned Businesses Report commissioned by American Express (www.womenable.com/70/the-state-of-women owned-businesses-in-the-u.s.:-2016) says that, excluding large, publicly traded firms, women-owned firms make up 38% of the privately held firm population, a
Living at home According to the U.S. American Community Survey (ACS), by 2014, for the first time in the history of the ACS, more U.S. 18- to 34-year-olds reported living with a parent than were living independently in their own homes. The survey found that 32.1% were living with parents vs. 31.6%
Polling disclaimer A newspaper article that reported the results of an election poll included the following explanation:The Associated Press poll on the 2016 presidential campaign is based on telephone interviews with 798 randomly selected registered voters from all states except Alaska and
Enough eggs? One of the important issues for poultry farmers is the production rate—the percentage of days on which a given hen actually lays an egg. Ideally, that would be 100% (an egg every day), but realistically, hens tend to lay eggs on about 3 of every 4 days. ISA Babcock wants to advertise
Cheating A Rutgers University study found that many high school students cheat on tests. The researchers surveyed a random sample of 4500 high school students nationwide; 74% of them said they had cheated at least once.1. Create a 90% confidence interval for the level of cheating among high school
Religion 2014 The 2014 U.S. Religious Landscape Study interviewed more than 35,000 Americans from all 50 states about their beliefs and the role of religion in their lives. The fastest-growing group is the 22.8% who are “Nones”—those who are not affiliated with any organized religion or have
Teen smoking 2015 The Centers for Disease Control and Prevention reports that 9.3% of surveyed high school students reported in 2015 that they had smoked cigarettes in the past 30 days. A college has 522 students in its freshman class. How likely is it that more than 10% of them are smokers?
Alcohol abuse Growing concern about binge drinking among college students has prompted one large state university to conduct a survey to assess the size of the problem on its campus. The university plans to randomly select students and ask how many have been drunk during the past week. If the
Errors An auto parts company advertises that its special oil additive will make the engine “run smoother, cleaner, longer, with fewer repairs.” An independent laboratory decides to test part of this claim. It arranges to have a taxicab company’s fleet of cars use the additive, and follows
Safety Observers in Texas watched children at play in eight communities. Of the 814 children seen biking, roller skating, or skateboarding, only 14% wore a helmet.1. Create and interpret an appropriate 95% confidence interval.2. What concerns do you have about this study that might make your
Fried PCs A computer company recently experienced a disastrous fire that ruined some of its inventory. Unfortunately, during the panic of the fire, some of the damaged computers were sent to another warehouse, where they were mixed with undamaged computers. The engineer responsible for quality
Power We are replicating an experiment. How will each of the following changes affect the power of our test? Indicate whether it will increase, decrease, or remain the same, assuming that all other aspects of the situation remain unchanged.1. We increase the number of subjects from 40 to 100.2. We
Grade inflation In 1996, 20% of all students at a major university had an overall grade point average of 3.5 or higher (on a scale of 4.0). In 2012, a random sample of 1100 student records found that 25% had a GPA of 3.5 or higher. Is this evidence of grade inflation?
Name recognition An advertising agency won’t sign an athlete to do product endorsements unless it is sure the person is known to more than 25% of its target audience. The agency always conducts a poll of 500 people to investigate the athlete’s name recognition before offering a contract. Then
Name recognition, part II The advertising company described in is thinking about signing a WNBA star to an endorsement deal. In its poll, 27% of the respondents could identify her. 1. Fans who never took statistics can’t understand why the company did not offer this WNBA player an endorsement
Women The U.S. Census Bureau reports that 36% of all U.S. businesses are owned by women (www.entrepreneur.com/article/252048). A Colorado consulting firm surveys a random sample of 410 businesses in the Denver area and finds that 164 of them have women owners. Should the firm conclude that its area
Speeding A newspaper report in August 2002 raised the issue of racial bias in the issuance of speeding tickets. The following facts were noted:. Sixteen percent of drivers registered in New Jersey are black.. Of the 324 speeding tickets issued in one month on a 65-mph section of the New Jersey
Meals A college student is on a “meal program.” His budget allows him to spend an average of $10 per day for the semester. He keeps track of his daily food expenses for 2 weeks; the data are given in the table below. Is there strong evidence that he will overspend his food allowance? Explain.
Occupy Wall Street In 2011, the Occupy Wall Street movement protested the concentration of wealth and power in the United States. A 2012 University of Delaware survey asked a random sample of 901 American adults whether they agreed or disagreed with the following statement:The Occupy Wall Street
Fritos® As a project for an Introductory Statistics course, students checked 6 bags of Fritos marked with a net weight of 35.4 grams. They carefully weighed the contents of each bag, recording the following weights (in grams): 35.5, 35.3, 35.1, 36.4, 35.4, 35.5. Is there evidence that the mean
And it means? Every statement about a confidence interval contains two parts—the level of confidence and the interval. Suppose that an insurance agent estimating the mean loss claimed by clients after home burglaries created the 95% confidence interval ($1644, $2391).1. What’s the margin of
Skin cancer In February 2012, MedPage Today reported that researchers used vemurafenib to treat metastatic melanoma (skin cancer). Out of 152 patients, 53% had a partial or complete response to vemurafenib.1. Write a 95% confidence interval for the proportion helped by the treatment, and interpret
Streams Researchers in the Adirondack Mountains collect data on a random sample of streams each year. One of the variables recorded is the substrate of the stream—the type of soil and rock over which they flow. The researchers found that 69 of the 172 sampled streams had a substrate of shale.
Final exam A statistics instructor created a linear regression equation to predict students’ final exam scores from their midterm exam scores. The regression equation was Fin^=10+0.9 Mid.1. If Susan scored a 70 on the midterm, what did the instructor predict for her score on the final?2. Susan
Traffic Highway planners investigated the relationship between traffic Density (number of automobiles per mile) and the average Speed of the traffic on a moderately large city thoroughfare. The data were collected at the same location at 10 different times over a span of 3 months. They found a mean
Crocodile lengths The ranges inhabited by the Indian gharial crocodile and the Australian saltwater crocodile overlap in Bangladesh. Suppose a very large crocodile skeleton is found there, and we wish to determine the species of the animal. Wildlife scientists have measured the lengths of the heads
Improving trees In the last exercise, you saw that the linear model had some deficiencies. Let’s create a better model.1. Perhaps the cross-sectional area of a tree would be a better predictor of its age. Since area is measured in square units, try re-expressing the data by squaring the
Depression and the Internet The September 1998 issue of the American Psychologist published an article by Kraut et al. that reported on an experiment examining “the social and psychological impact of the Internet on 169 people in 73 households during their first 1 to 2 years online.” In the
Gasoline Since clean-air regulations have dictated the use of unleaded gasoline, the supply of leaded gas in New York state has diminished. The following table was given on the August 2001 New York State Math B exam, a statewide achievement test for high school students.1. Create a linear model and
Tobacco and alcohol Are people who use tobacco products more likely to consume alcohol? Here are data on household spending (in pounds) taken by the British government on 11 regions in Great Britain. Do tobacco and alcohol spending appear to be related? What questions do you have about these data?
Williams football The Sears Cup was established in 1993 to honor institutions that maintain a broad-based athletic program, achieving success in many sports, both men’s and women’s. In the years following its Division III inception in 1995, the cup was won by Williams College 15 of 17 years.
Down the drain Most water tanks have a drain plug so that the tank may be emptied when it’s to be moved or repaired. How long it takes a certain size of tank to drain depends on the size of the plug, as shown in the table. Create a model. Plug Dia (in.) 38 12 341 114 112 2 Drain Time (min) 140 80
Chips A start-up company has developed an improved electronic chip for use in laboratory equipment. The company needs to project the manufacturing cost, so it develops a spreadsheet model that takes into account the purchase of production equipment, overhead, raw materials, depreciation,
Satisfied workers The managers of a large company wished to know the percentage of employees who feel “extremely satisfied” to work there. The company has roughly 24,000 employees. They contacted a random sample of employees and asked them about their job satisfaction, obtaining 437 completed

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Stats Data And Models 5th Edition Richard D De Veaux, Paul F Velleman, David E Bock - Solutions

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