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inferential statistics
Intro Stats 6th Edition Richard D. De Veaux, Paul F. Velleman, David Bock - Solutions
More repairs Consider again the auto repair rates described in Exercise 39. If you own two cars, what is the probability thata) neither will need repair?b) both will need repair?c) at least one car will need repair?
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 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 needa) no repairs?b) no more than one
College admissions II In Exercise 37 we saw that in 2015 Harvard accepted about 5.3% of its applicants, Dartmouth 10%, and Penn 9.9%. Jorge has applied to all three. He figures that his chances of getting into at least one of the three must be about 25.2%.a) How has he arrived at this conclusion?b)
College admissions 2015 For high school students graduating in 2015, college admissions to the nation’s most selective schools were the most competitive in memory. Harvard accepted about 5.3% of its applicants, Dartmouth 10%, and Penn 9.9%. Jorge has applied to all three. Assuming that he’s a
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?
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?
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
Online banking last time Given the probabilities in Exercise 18, 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?
Facebook final Given the probabilities in Exercise 17, 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?
Online banking again Suppose that the information in Exercise 18 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 17 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, threesevenths log on every day. Draw a tree for this
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 70% of its users are from outside the United States and that 50% of its users log on to Facebook every day. Suppose that 20% of its users are U.S.users who log on every day. Make a probability table. Why is a table better than a tree here?
Births If the sex of a child is independent of all other births, is the probability of a woman giving birth to a girl after having four boys greater than it was on her first birth? Explain.
Titanic On the Titanic, the probability of survival was 0.323.Among first class passengers, it was 0.625. Were survival and ticket class independent? Explain.
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 train 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 train. What is the probability that it will cause him to miss the train?
Sports again From Exercise 11, if someone doesn’t like to watch basketball, what is the probability that she will be a football fan?
Sports What is the probability that a person likes to watch football, given that she also likes to watch basketball?EXERCISES Football No Football Basketball 27 13 No Basketball 38 22
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?
Cell phones and surveys The survey by the National Center for Health Statistics further found that 71% 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 only a cell phone and no
Landlines and surveys A 2015 study conducted by the National Center for Health Statistics (www.cdc.gov/nchs/data/nhis/earlyrelease/wireless201512.pdf) found that 51% of U.S.households had no landline service. This raises concerns about the accuracy of certain surveys, as they depend on random-digit
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.
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 Flipping a fair coin is said to randomly generate heads and tails with equal probability. Explain what random means in this context.
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
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
Fuel efficiency Wayne Collier designed an experiment to measure the fuel efficiency of his family car under different tire pressures. For each run, he set the tire pressure to either 28 or 32 psi and then measured the miles driven on a highway (I-95 between Mills River and Pisgah Forest, NC) until
Acupuncture Research reported in 2008 brings to light the effectiveness of treating chronic lower back pain with different methods. One-third of nearly 1200 volunteers were administered conventional treatment (drugs, physical therapy, and exercise). The remaining patients got 30-minute acupuncture
Bats It’s generally believed that baseball players can hit the ball farther with aluminum bats than with the traditional wooden ones. Is that true? And, if so, how much farther?Players on your local high school baseball team have agreed to help you find out. Design an appropriate experiment.
Save the grapes Vineyard owners have problems with birds that like to eat the ripening grapes. Some vineyards use scarecrows to try to keep birds away. Others use netting
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
Age and party 2008 The Pew Research Center collected data from national exits polls conducted by NBC News after the 2008 presidential election. The following table shows information regarding voter age and party preference:a) What sampling strategy do you think the pollsters used?Explain.b) What
Pubs In England, a Leeds University researcher said that the local watering hole’s welcoming atmosphere helps men get rid of the stresses of modern life and is vital for their psychological well-being. Author of the report, Dr. Colin Gill, said rather than complain, women should encourage men to
Sex and violence Does the content of a television program affect viewers’ memory of the products advertised in commercials? Design an experiment to compare the ability of viewers to recall brand names of items featured in commercials during programs with violent content, sexual content, or
Antacids A researcher wants to compare the performance of three types of antacid in volunteers suffering from acid reflux disease. Because males and females may react differently to this medication, the subjects are split into two groups, by gender. Subjects in each group are randomly assigned to
Smoking and Alzheimer’s Medical studies indicate that smokers are less likely to develop Alzheimer’s disease than people who never smoked.a) Does this prove that smoking may offer some protection against Alzheimer’s? Explain.b) Offer an alternative explanation for this association.c) How
Youthful appearance Readers’ Digest (April 2002, p. 152)reported results of several surveys that asked graduate students to examine photographs of men and women and try to guess their ages. Researchers compared these guesses with the number of times the people in the pictures reported having
Homecoming A college statistics class conducted a survey concerning community attitudes about the college’s large homecoming celebration. That survey drew its sample in the following manner: Telephone numbers were generated at random by selecting one of the local telephone exchanges(first three
Cookies Mary Beth, Nigel, and Molly want to design an experiment to find the recipe for the best chocolate chip cookies. They will try to keep the size of the cookies the same, but use cooking times of 10 and 15 minutes. They will use three different temperatures: 325°F, 375°F and 425°F and use
How long is 30 seconds? Sofie, Ryan, and Alessandra wanted to design an experiment to find out how distraction affects our ability to judge time. The experiment consisted of starting a clock (out of view of the subject) and then asking the subject to tell them when they thought 30 seconds had
Laundry An experiment to test a new laundry detergent, SparkleKleen, is being conducted by a consumer advocate group. They would like to compare its performance with that of a laboratory standard detergent they have used in previous experiments. They can stain 16 swatches of cloth with 2 tsp of a
Timing In August 2011, a Sodahead.com voluntary response poll asked site visitors, “Obama is on Vacation Again: Does He Have the Worst Timing Ever?” 56% of the 629 votes were for “Yes.” During the week of the poll, a 5.8 earthquake struck near Washington, D.C., and Hurricane Irene made its
Tips, take 2 In another experiment to see if getting candy after a meal would induce customers to leave a bigger tip, a server randomly decided how to treat 80 dining parties.Some parties received no candy, some just one piece, and some two pieces. Others initially got just one piece of candy, and
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 servers determined randomly whether or not to give candy to 92 dining parties. They recorded the sizes of the tips and reported that guests getting candy
Cell phone risks Researchers at the Washington University School of Medicine randomly placed 480 rats into one of three chambers containing radio antennas. One group was exposed to digital cell phone radio waves, the second to analog cell phone waves, and the third group to no radio waves. Two
Alternate-day fasting A paper published in 2017 in JAMA Internal Medicine (jamanetwork.com/journals/jamainternalmedicine/fullarticle/2623528) reported on a study of alternate-day fasting as a weight-loss method. One hundred obese persons were assigned at random to one of three groups: an
Compare the histograms of the samples to a histogram of the full data. Write a brief report on what you conclude. What attributes of the full data distribution can you see in the samples? Which ones are harder to see?
Samples of bridges Use the statistics package of your choice or the simple sample tool at astools.datadesk.com to draw samples of the conditions from the New York Bridges 2016 data file. Draw a sample of 50, a sample of 100, a sample of 200, and a sample of
Commuter sample The data file Commute times sample 100 holds a sample drawn from the Commute times dataset. Using your statistics program, make histograms of the sample and the population. Discuss how they are similar and how they differ.
Does the use of computer software in introductory statistics classes lead to better understanding of the concepts? A professor teaching two sections of statistics decides to investigate. She teaches both sections using the same lectures and assignments, but gives one class statistics software to
Older Americans with a college education are significantly more likely to be emotionally well-off than are people in this age group with less education. Among those aged 65 and older, 35% scored 90 or above on the Emotional Health Index, but for those with a college degree, the percentage rose to
A soft-drink manufacturer must be sure the bottle caps on the soda are fully sealed and will not come off easily. Inspectors pull a few bottles off the production line at regular intervals and test the caps. If they detect any problems, they will stop the bottling process to adjust or repair the
An orange-juice processing plant will accept a shipment of fruit only after several hundred oranges selected from various locations within the truck are carefully inspected. If too many show signs of unsuitability for juice (bruised, rotten, unripe, etc.), the whole truckload is rejected.
People aged 50 to 71 were initially contacted in the mid1990s to participate in a study about smoking and bladder cancer. Data were collected from more than 280,000 men and 186,000 women from eight states who answered questions about their health, smoking history, alcohol intake, diet, physical
Tests of gene therapy on laboratory rats have raised hopes of stopping the degeneration of tissue that characterizes chronic heart failure. Researchers at the University of California, San Diego, used hamsters with cardiac disease, randomly assigning 30 to receive the gene therapy and leaving the
An artisan wants to create pottery that has the appearance of age. He prepares several samples of clay with four different glazes and test fires them in a kiln at three different temperature settings.
Widely used antidepressants may reduce ominous brain plaques associated with Alzheimer’s disease. In the study, mice genetically engineered to have large amounts of brain plaque were given a class of antidepressants that boost serotonin in the brain. After a single dose, the plaque levels
Some doctors have expressed concern that men who have vasectomies seemed more likely to develop prostate cancer.Medical researchers used a national cancer registry to identify 923 men who had had prostate cancer and 1224 men of similar ages who had not. Roughly one quarter of the men in each group
Does keeping a child’s lunch in an insulated bag, even with ice packs, protect the food from warming to temperatures where germs can proliferate? Researchers used an electric temperature gun on 235 lunches at preschools 90 minutes before they were to be eaten. Of the lunches with ice packs, over
People who read the last page of a mystery novel first generally like stories better. Researchers recruited 819 college students to read short stories, and for one story, they were given a spoiler paragraph beforehand. On the second and third story, the spoiler was incorporated as the opening
Fireworks manufacturers face a dilemma. They must be sure that the rockets work properly, but test-firing a rocket essentially destroys it. On the other hand, not testing the product leaves open the danger that they sell a bunch of duds, leading to unhappy customers and loss of future sales. The
In the journal Science, a research team reported that plants in southern England are flowering earlier in the spring.Records of the first flowering dates for 385 species over a period of 47 years indicate that flowering has advanced an average of 15 days per decade, an indication of climate
Data were collected over a decade from 1021 men and women with a recent history of precancerous colon polyps.Participants were randomly assigned to receive folic acid(a B vitamin) or a placebo, and the study concluded that those receiving the folic acid may actually increase their risk of
The radioactive gas radon, found in some homes, poses a health risk to residents. To assess the level of contamination in their area, a county health department wants to test a few homes. If the risk seems high, they will publicize the results to emphasize the need for home testing. Officials plan
Researchers at the Purina Pet Institute studied Labrador retrievers for evidence of a relationship between diet and longevity. At 8 weeks of age, 2 puppies of the same sex and weight were randomly assigned to one of two groups—a total of 48 dogs in all. One group was allowed to eat all they
The journal Circulation reported that among 1900 people who had heart attacks, those who drank an average of 19 cups of tea a week were 44% more likely than nondrinkers to survive at least 3 years after the attack.
Researchers identified 242 children in the Cleveland area who had been born prematurely (at about 29 weeks). They examined these children at age 8 and again at age 20, comparing them to another group of 233 children not born prematurely. Their report, published in the New England Journal of
Skydiving, anyone? A humor piece published in the British Medical Journal (“Parachute use to prevent death and major trauma related to gravitational challenge: Systematic review of randomized control trials,” Gordon, Smith, and Pell, BMJ, 2003:327) notes that we can’t tell for sure whether
Washing clothes A consumer group wants to test the effectiveness of a new “organic” laundry detergent and make recommendations to customers about how to best use the product. They intentionally stain 30 white T-shirts with grass in order to see how well the detergent will clean them. They want
Safety switch An industrial machine requires an emergency shutoff switch that must be designed so that it can be easily operated with either hand. Design an experiment to find out whether workers will be able to deactivate the machine as quickly with their left hands as with their right hands. Be
SAT prep Can special study courses actually help raise SAT scores? One organization says that the 30 students they tutored achieved an average gain of 60 points when they retook the test.a) Explain why this does not necessarily prove that the special course caused the scores to go up.b) Propose a
Beetles Hoping to learn how to control crop damage by a certain species of beetle, a researcher plans to test two different pesticides in small plots of corn. A few days after application of the chemicals, he’ll check the number of beetle larvae found on each plant. The researcher wants to know
Shingles A research doctor has discovered a new ointment that she believes will be more effective than the current medication in the treatment of shingles (a painful skin rash). Eight patients have volunteered to participate in the initial trials of this ointment. You are the statistician hired as
Weekend deaths A study published in the New England Journal of Medicine (Aug. 2001) suggests that it’s dangerous to enter a hospital on a weekend. During a 10-year period, researchers tracked over 4 million emergency admissions to hospitals in Ontario, Canada. Their findings revealed that
Gas mileage Do cars get better gas mileage with premium instead of regular unleaded gasoline? It might be possible to test some engines in a laboratory, but we’d rather use real cars and real drivers in real day-to-day driving, so we get 20 volunteers.Design the experiment.
Reading Some schools teach reading using phonics (the sounds made by letters) and others using whole language (word recognition). Suppose a school district wants to know which method works better. Suggest a design for an appropriate experiment.
Healing A medical researcher suspects that giving postsurgical patients large doses of vitamin E will speed their recovery times by helping their incisions heal more quickly.Design an experiment to test this conjecture. Be sure to identify the factors, levels, treatments, response variable, and 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 20 identical containers, fill some with water, and
Swimming Recently, a group of adults who swim regularly for exercise were evaluated for depression. It turned out that these swimmers were less likely to be depressed than the general population. The researchers said the difference was statistically significant.a) What does “statistically
Wine A 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
Contrast baths 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)
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 Dietary Approaches to Stop Hypertension (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
Hamstrings Exercise 33 discussed an experiment to see if the time it took athletes with hamstring injuries to be able to return to sports was different depending on which of two exercise programs they engaged in.a) Explain why it was important to assign the athletes to the two different treatments
Swimsuits A swimsuit manufacturer wants to test the speed of its newly designed suit. The company designs an experiment by having 6 randomly selected Olympic swimmers swim as fast as they can with their old swimsuit first and then swim the same event again with the new, expensive swimsuit. The
Shoes A running-shoe manufacturer wants to test the effect of its new sprinting shoe on 100-meter dash times. The company sponsors 5 athletes who are running the 100-meter dash in the 2012 Summer Olympic games. To test the shoe, it has all 5 runners run the 100-meter dash with a competitor’s shoe
Tomatoes II Describe a strategy to randomly split 24 tomato plants into the three groups for the completely randomized single-factor experiment of Exercise 4.
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