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intro stats
Stats Data And Models 5th Global Edition Richard De Veaux, Paul Velleman, David Bock - Solutions
More repairs Consider again the auto repair rates described in Exercise
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 students
Car repairs A consumer organization estimates that over a 1-year period, 20% of cars will need to be repaired only once, 5% will need repairs exactly twice, and 2% of cars will require three or more repairs. What is the probability that a car chosen at random will needa) no repairs?b) no more than
University admissions In Exercise 25, we see that for the incoming class of 2023, three of the top universities accepted 4.5%, 5.91%, and 5.77% of their applicants, respectively. Noah applied to all three. He figures that his chances of getting into at least one of them must be about 16.18%.a) How
University admissions For the incoming class of 2023, university admissions for the most selective universities were extremely competitive. Three of these universities accepted 4.5%, 5.91%, and 5.77% of their applicants, respectively.Noah applied to all three. Assuming that he is a typical
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
Speeders 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?
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
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?
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 totaled 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 color that will determine what happens next. Which of the following probability assignments are legitimate? 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
Auto insurance 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?
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 tennis player loses 4 out of the first 5 games in a set against an equally skilled opponent, where the odds give the tennis player a 50% chance of both winning and losing.However, he is extremely confident that he will win his next game. Comment on his 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 been
Rain The weather reporter on TV makes predictions such as a 25% chance of rain. What do you think is the meaning of such a phrase?
Roulette A casino claims that its roulette wheel is truly random.What should that claim mean?
Sample spaces For each of the following, list the sample space and tell whether you think the events are equally likely:a) Roll two dice; record the sum of the numbers.b) A family has 3 children; record each child’s sex in order of birth.c) Toss four coins; record the number of tails.d) Toss a
Sample spaces For each of the following, list the sample space and tell whether you think the events are equally likely:a) Toss 2 coins; record the order of heads and tails.b) A family has 3 children; record the number of boys.c) Flip a coin until you get a head or 3 consecutive tails; record each
Cell phones and surveys II A 2017 report by the National Health Interview Survey claims that 53.3% of adults in American homes used only wireless service (and no landline).We randomly select six adults:a) What is the probability that all of these adults had a landline?b) What is the probability
Cell phones and surveys A 2018 study conducted by the Australian Communications and Media Authority found that 31%of Australian households had no fixed landline at home. This raises concerns about the accuracy of certain surveys, as they depend on random-digit dialing to households via
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.
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 50 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 used to decrease the severity of shingles and the pain level associated with this skin rash. Eight patients have volunteered to participate in the initial trials of this
Weekend deaths A study suggests that it’s dangerous to enter a hospital on a weekend. During a six-year period, researchers tracked over 1 million emergency admissions to hospitals in a certain region. Their findings revealed that patients admitted on weekends had a much higher risk of death than
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 34 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 the
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 28 identical containers, fill half of them with
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
Mozart Will listening to a Mozart piano sonata make you smarter? In a 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
Diet and blood pressure An experiment showed that subjects fed the Paleo diet were able to lower their blood pressure by an average of 5.7 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 their newly designed suit. The company designs an experiment by having 13 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
Omega-3, finis Exercises 21, 35, and 37 describe an experiment investigating the effectiveness of omega-3 fats in treating bipolar disorder. Suppose some of the 30 subjects were very active people who walked a lot or got vigorous exercise several times a week, while others tended to be more
Insomnia, again Exercises 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-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
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 50.2 days faster than those assigned to a program of agility and trunk stabilization exercises.
A pet supply company wants to compare a new lower-calorie food with their standard horse food to see if it’s effective in helping inactive horses lower blood pressure. They have found several horse owners willing to participate in the trial. The horses have been classified as small (1000 lbs)
Some people claim they can get relief from sharp neck pain by drinking a large glass of ice-cold water. Researchers plan to enlist several people who suffer from sharp neck pain in a test. When a participant experiences a sharp neck pain, 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
A science journal reported that, contrary to popular belief, depressed individuals cry no more often in response to sad situations than nondepressed people. Researchers studied 65 women and 32 men with major depression and 71 men and 35 women with no depression. They showed the subjects a sad film
They found no evidence of benefits associated with the medicine.
Scientists at a major pharmaceutical firm investigated the effectiveness of a new medicine to treat the measles. They exposed each subject to a measles virus, then gave him or her either the new medicine or a sugar solution known to have no effect on measles. Several days later, they assessed the
A popular science magazine reported that a study of women in Finland indicated that having sons shortened the life spans of mothers by about 25 weeks per son, but that daughters helped to lengthen the mothers’ lives. The data came from church records from the period 1623 to 1724.
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. (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
There is some concern that if women over the age of 57 who take supplemental hormones also drink alcohol, their hormone levels will drop too low. Twelve volunteers who were receiving supplemental estrogen were randomly divided into two groups, as were 13 other volunteers not on estrogen. In each
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
In a test of roughly 560 widows, 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.
Among a group of disabled women aged 60 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.
Over a five-month period, among 72 people with bipolar disorder, patients who were given a 626 mg/day dose of omega-3 fats from fish oil improved more than those given a placebo.
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 393 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 adults whether they planned to watch the upcoming Super Bowl. Men and women were asked separately whether they were looking
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 190 exchange
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
Tomatoes finis What factors might confound the results of the experiment in Exercise 4?
Confounded tips For the experiment of Exercise 3, name some confounding variables that might influence the experiment’s results.
Blocking tomatoes To obtain enough plants for the tomato experiment of Exercise 4, experimenters have to purchase plants from two different garden centers. They then randomly assign the plants from each garden center to all three fertilizer treatments. Is the experiment blocked? Is that a good idea?
Block that tip The driver of Exercise 3 wants to know about tipping in general. So he recruits several other drivers to participate in the experiment. Each driver randomly decides whether to phone customers before delivery and records the tip percentage. Is this experiment blocked? Is that a good
More tomatoes If the tomato taster doesn’t know how the tomatoes have been treated, is the experiment single- or doubleblind?How might the blinding be improved further?
More tips Is the experiment of Exercise 3 blind? Can it be double-blind? Explain.
Tomatoes again For the experiment of Exercise 4, discuss variables that could be controlled or that could not be controlled.Is the experiment randomized and replicated?
Tips again For the experiment of Exercise 3, name some variables the driver did or should have controlled. Was the experiment randomized and replicated?
Tomatoes II For the experiment described in Exercise 4, name the factor and its levels. How might the response be measured?
Tips II For the experiment described in Exercise 3, list the factor, the levels, and the response variable.
Tomatoes You want to compare the tastiness and juiciness of tomatoes grown with three amounts of a new fertilizer: none, half the recommended amount, and the full recommended amount. You allocate 24 tomato plants to receive each amount of fertilizer, assigning them at random. What are the
Tips 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 away, hoping this slight bump in customer service will lead to a slight bump in tips.
E-commerce A business student conjectures that the Internet caused companies to become more profitable, since many transactions previously handled “face-to-face” could now be completed online. The student compares earnings from a sample of companies from the 1980s to a sample from the 2010s.
Steroids The 1990s and early 2000s could be considered the steroids era in Major League Baseball, as many players have admitted to using the drug to increase performance on the field.If a sports writer wanted to compare home run totals from the steroids era to an earlier decade, say the 1960s,
More sampling methods Consider each of these situations. Do you think the proposed sampling method is appropriate? Explain.a) We want to know if there is neighborhood support to turn a vacant lot into a playground. We spend a Saturday afternoon going door-to-door in the neighborhood, asking people
Sampling methods Consider each of these situations. Do you think the proposed sampling method is appropriate? Explain.a) We want to know what percentage of local doctors accept patients who avail state-sponsored medical assistance. We call the offices of 75 doctors randomly selected from local
Another fish story In recent years, beaches around the world have seen fish washing up on shore in large numbers. One group of scientists thought that leakage from the damaged Fukushima nuclear power plant in Japan might be a cause. They propose to measure the mean amount of radiation in a sample
A fish story Concerned about reports of discolored scales on fish caught downstream from a newly sited chemical plant, scientists set up a field station in a shoreline public park. For one week, they asked fishermen there to bring any fish they caught to the field station for a brief inspection. At
Quality control Sammy’s Salsa, a small local company, produces 20 cases of salsa a day. Each case contains 12 jars and is imprinted with a code indicating the date and batch number.To help maintain consistency, at the end of each day, Sammy selects three jars of salsa, weighs the contents, and
Happy workers? A manufacturing company employs 14 project managers, 370 supervisors, and 388 laborers. In an effort to keep informed about any possible sources of employee discontent, management wants to conduct job satisfaction interviews with a sample of employees every month.a) Do you see any
Accounting Between quarterly audits, a company likes to check on its accounting procedures to address any problems before they become serious. The accounting staff processes payments on about 120 orders each day. The next day, the supervisor rechecks 10 of the transactions to be sure they were
Fuel economy Occasionally, when I fill my car with gas, I figure out how many miles per gallon my car got. I wrote down those results after six fill-ups in the past few months. Overall, it appears my car gets 28.1 miles per gallon.a) What statistic have I calculated?b) What is the parameter I’m
Arm length How long is your arm compared with your hand size? Put your right thumb at your left shoulder bone, stretch your hand open wide, and extend your hand down your arm. Put your thumb at the place where your little finger is, and extend down the arm again. Repeat this a third time. Now your
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