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inferential statistics
Intro Stats 6th Edition Richard D. De Veaux, Paul F. Velleman, David Bock - Solutions
Pilot study A state’s environmental agency worries that many cars may be violating clean air emissions standards. The agency hopes to check a sample of vehicles in order to estimate that percentage with a margin of error of 3% and 90% confidence.To gauge the size of the problem, the agency first
Better hiring info Editors of the business report in Exercise 20 are willing to accept a margin of error of 4% but want 99%confidence. How many randomly selected employers will they need to contact?
Graduation, again As in Exercise 19, we hope to estimate the percentage of adults aged 25 to 30 who never graduated from high school. What sample size would allow us to increase our confidence level to 95% while reducing the margin of error to only 2%?
Back to campus II Suppose ACT, Inc. wants to update their information from Exercise 46 on the percentage of first-years that return for a second year of college.a) They want to cut the stated margin of error in half. How many college first-years must be surveyed?b) Do you have any concerns about
Deer ticks Wildlife biologists inspect 153 deer taken by hunters and find 32 of them carrying ticks that test positive for Lyme disease.a) Create a 90% confidence interval for the percentage of deer that may carry such ticks.b) If the scientists want to cut the margin of error in half, how many
Back to campus ACT, Inc. reported that 74% of 1644 randomly selected college first-years returned to college the next year.The study was stratified by type of college—public or private.The retention rates were 71.9% among 505 students enrolled in public colleges and 74.9% among 1139 students
Higher ed post-COVID In June 2020, a survey of 97 college presidents by Inside Higher Ed and Hanover Research showed that 68% were concerned about faculty readiness to conduct online learning or hybrid learning.
Speech transcriptions In a study comparing speech-to-text transcription services, researchers estimated the accuracy rate of YouTube’s auto-transcription service to be 72% (28% of words were incorrectly transcribed), with a 95% confidence interval of (67.8%, 75.5%).a) Interpret this interval in
Rickets Vitamin D, whether ingested as a dietary supplement or produced naturally when sunlight falls on the skin, is essential for strong, healthy bones. The bone disease rickets was largely eliminated in England during the 1950s, but now there is concern that a generation of children more likely
Gambling A city ballot includes a local initiative that would legalize gambling. The issue is hotly contested, and two groups decide to conduct polls to predict the outcome. The local newspaper finds that 53% of 1200 randomly selected voters plan to vote “yes,” while a college statistics class
Death penalty, again In a previous survey on the death penalty such as the one you read about in the Step-by-Step Example, the Gallup Poll split the sample at random, asking 510 respondents, “Generally speaking, do you believe the death penalty is applied fairly or unfairly in this country
Local news The mayor of a small city has suggested that the state locate a new prison there, arguing that the construction project and resulting jobs will be good for the local economy.A total of 183 residents show up for a public hearing on the proposal, and a show of hands finds only 31 in favor
Safe food Some food retailers propose subjecting food to a low level of radiation in order to improve safety, but the sale of such “irradiated” food is opposed by many people. Suppose a grocer wants to find out what his customers think. He has cashiers distribute surveys at checkout and ask
Junk mail Direct mail advertisers send solicitations (a.k.a.“junk mail”) to thousands of potential customers in the hope that some will buy the company’s product. The acceptance rate is usually quite low. Suppose a company wants to test the response to a new flyer, and sends it to 1000 people
Teenage drivers An insurance company checks police records on 582 accidents selected at random and notes that teenagers were at the wheel in 91 of them.a) Create a 95% confidence interval for the percentage of all auto accidents that involve teenage drivers.b) Explain what your interval means.c)
Take the offer First USA, a major credit card company, is planning a new offer for their current cardholders. The offer will give double airline miles on purchases for the next 6 months if the cardholder goes online and registers for the offer. To test the effectiveness of the campaign, First USA
Contributions, please The Paralyzed Veterans of America is a philanthropic organization that relies on contributions.They send free mailing labels and greeting cards to potential donors on their list and ask for a voluntary contribution.To test a new campaign, they recently sent letters to a random
Still living online The Pew Research poll described in Exercise 5 found that 45% of a sample of 1058 teens are online almost constantly. (Treat this as a simple random sample.)a) Find the margin of error for this poll if we want 95% confidence in our estimate of the percent of American teens who go
Baseball fans In a poll taken in December 2012, Gallup asked 1006 U.S. adults whether they were baseball fans; 48%said they were. Almost five years earlier, in February 2008, only 35% of a similar-size sample had reported being baseball fans.a) Find the margin of error for the 2012 poll if we want
Mislabeled seafood, second course A Consumer Reports study similar to the one described in Exercise 31 found that 12 of the 22 “red snapper” packages tested were actually a different kind of fish.a) Are the conditions for creating a confidence interval satisfied? Explain.b) Construct a 95%
Mislabeled seafood The environmental group Oceana(usa.oceana.org) analyzed 1215 samples of seafood purchased across the United States and genetically compared the pieces to standard gene fragments that can identify the species.Laboratory results indicated that 33% of the seafood was mislabeled
Parole A study of 902 decisions (to grant parole or not) made by the Nebraska Board of Parole produced the following computer output. Assuming these cases are representative of all cases that may come before the Board, what can you conclude?z-Interval for proportion With 95.00% confidence,
Cars What fraction of cars are made in Japan? The computer output below summarizes the results of a random sample of 50 autos. Explain carefully what it tells you.z-Interval for proportion With 90.00% confidence, 0.29938661 6 P(japan) 6 0.46984416
Confidence intervals, again Several factors are involved in the creation of a confidence interval. Among them are the sample size, the level of confidence, and the margin of error. Which statements are true?a) For a given sample size, reducing the margin of error will mean lower confidence.b) For a
Confidence intervals Several factors are involved in the creation of a confidence interval. Among them are the sample size, the level of confidence, and the margin of error. Which statements are true?a) For a given sample size, higher confidence means a smaller margin of error.b) For a specified
More conclusions Two students made worldwide headlines by spinning a Belgian euro 250 times and getting 140 heads—that’s 56%. That makes the 90% confidence interval (51%, 61%).What does this mean? Are these conclusions correct? Explain.a) Between 51% and 61% of all euros are unfair.b) We are
Conclusions A catalog sales company promises to deliver orders placed on the Internet within 3 days. Follow-up calls to a few randomly selected customers show that a 95% confidence interval for the proportion of all orders that arrive on time is 88% { 6%. What does this mean? Are these conclusions
More conditions Consider each situation described. Identify the population and the sample, explain what p and pn represent, and tell whether the methods of this chapter can be used to create a confidence interval.a) A consumer group hoping to assess customer experiences with auto dealers surveys
Conditions For each situation described below, identify the population and the sample, explain what p and pn represent, and tell whether the methods of this chapter can be used to create a confidence interval.a) Police set up an auto checkpoint at which drivers are stopped and their cars inspected
Another margin of error A medical researcher estimates the percentage of children exposed to lead-based paint, adding that he believes his estimate has a margin of error of about 3%.Explain what the margin of error means.
Margin of error A TV newscaster reports the results of a poll of voters, and then says, “The margin of error is plus or minus 4%.” Explain carefully what that means.
Hiring In preparing a report on the economy, we need to estimate the percentage of businesses that plan to hire additional employees in the next 60 days.a) How many randomly selected employers must we contact in order to create an estimate in which we are 98% confident with a margin of error of 5%?
Graduation It’s believed that as many as 25% of adults over 50 never graduated from high school. We wish to see if this percentage is the same among the 25 to 30 age group.a) How many of this younger age group must we survey in order to estimate the proportion of non-grads to within 6%with 90%
More Exodus in Exercise 16 we saw that 52% of surveyed Californians considered moving out of the state.a) Are the conditions for constructing a confidence interval met?b) Would the margin of error be larger or smaller for 95%confidence?
Wrong direction again Consider the poll of Exercise 15.a) Are the assumptions and conditions met?b) Would the margin of error be larger or smaller for 95%confidence? Explain.
California Exodus? A poll conducted by the UC Berkeley Institute of Governmental Studies in 2019 found that 52% of 4527 respondents said they considered moving out of the
Wrong direction A Morning Consult/Politico poll of 1997 registered voters in July 2020 asked a standard polling question of whether the United States was headed in the“Right Direction” or was on the “Wrong Track.” 75% said that things are on the wrong track vs. 25% who said “right
Family variety In a 2019 Pew Research study on trends in marriage and family (www.pewsocialtrends.org/2015/12/17/1-theamerican-family-today/), 30% of randomly surveyed adults say that the growing variety of family arrangements is a “good thing.” The 95% confidence interval is from 29.1% to
Still living online The 95% confidence interval for the proportion of teens in Exercise 5 who reported that they went online several times daily is from 42% to 48%.a) Interpret the interval in this context.b) Explain the meaning of “95% confident” in this context.
Soup A machine is supposed to fill cans with 16 oz of soup.Of course, there will be some variation in the amount actually dispensed, and measurement errors are often approximately normally distributed. The manager would like to understand the variability of the variances of the samples, so he
Sample maximum The distribution of scores on a statistics test for a particular class is skewed to the left. The professor wants to predict the maximum score and so wants to understand the distribution of the sample maximum. She simulates the distribution of the maximum of the test for 30 different
Character recognition, again The automatic character recognition device discussed in Exercise 4 successfully reads about 85% of handwritten credit card applications. In Exercise 4, you looked at the histograms showing distributions of sample proportions from 1000 simulated samples of size 20, 50,
Send more money The philanthropic organization in Exercise 3 expects about a 5% success rate when they send fundraising letters to the people on their mailing list. In Exercise 3, you looked at the histograms showing distributions of sample proportions from 1000 simulated mailings for samples of
Campus sample For her final project, Stacy plans on surveying a random sample of 50 students on whether they plan to go to Florida for spring break. From past years, she guesses that about 10% of the class goes. Is it reasonable for her to use a Normal model for the sampling distribution of the
Marriage According to a Pew Research survey, 27% of American adults are pessimistic about the future of marriage and the family. That is based on a random sample of about 1500 people. Is it reasonable for Pew Research to use a Normal model for the sampling distribution of the sample proportion?Why
How’s life? Gallup regularly conducts a poll using a“Cantril scale,” which asks respondents to imagine a ladder with 10 rungs. Rung 0 represents the worst possible life, and rung 10 represents the best possible life. Respondents are asked what rung they would say they are on. Responses are
Living online Pew Research, in 2018, polled a random sample of 1058 U.S. teens (ages 13–17) about Internet use. 45%reported that they were online “almost constantly”—a fact of great interest to advertisers.
Character recognition An automatic character recognition device can successfully read about 85% of handwritten credit card applications. To estimate what might happen when this device reads a stack of applications, the company did a simulation using samples of size 20, 50, 75, and 100. For each
Send money When they send out their fundraising letters, a philanthropic organization typically gets a return from about 5% of the people on their mailing list. To see what the response rate might be for future appeals, they did a simulation using samples of size 20, 50, 100, and 200. For each
Marketing The proportion of adult women in the United States is approximately 51%. A marketing survey telephones 400 people at random.a) What proportion of the sample of 400 would you expect to be women?b) What would the standard deviation of the sampling distribution be?c) How many women, on
Website An investment company is planning to upgrade the mobile access to their website, and they’d like to know the proportion of their customers who access it from their smartphones. They draw a random sample of 200 from customers who recently logged in. Suppose that the true proportion of
COVID-19 Antibody Testing, continued. Consider the COVID-19 antibody test in the previous exercise. If 2% of the entire population have antibodies, and you test negative, what is the probability that you actually do have antibodies?
COVID-19 Antibody Testing The first FDA-approved COVID-19 antibody test, Cellex, has a 94% chance of being right (testing positive for antibodies) when used by people with antibodies, and 96% chance of being right (testing negative for antibodies) when used by people without antibodies.Suppose you
Facial analysis system errors, II A study conducted by researchers at MIT and the University of Toronto found that Amazon’s facial analysis software Rekognition, used by some local governments for tracking down suspects, routinely mislabeled dark-skinned men as women 1% of the time, and almost
Facial analysis system errors. A study conducted by researchers at MIT and the University of Toronto found that Amazon’s facial analysis software Rekognition, used by some local governments for tracking down suspects, routinely mislabeled dark-skinned women as men 31% of the time, and routinely
Polygraphs Lie detectors are controversial instruments, barred from use as evidence in many courts. Nonetheless, many employers use lie detector screening as part of their hiring process in the hope that they can avoid hiring people who might be dishonest. There has been some research, but no
HIV testing In July 2005, the journal Annals of Internal Medicine published a report on the reliability of HIV testing. Results of a large study suggested that among people with HIV, 99.7% of tests conducted were (correctly) positive, while for people without HIV 98.5% of the tests were (correctly)
Parts A company manufacturing electronic components for home entertainment systems buys electrical connectors from three suppliers. The company prefers to use supplier A because only 1% of those connectors prove to be defective, but supplier A can deliver only 70% of the connectors needed. The
Dishwashers Dan’s Diner employs three dishwashers. Al washes 40% of the dishes and breaks only 1% of those he handles. Betty and Chuck each wash 30% of the dishes, and Betty breaks only 1% of hers, but Chuck breaks 3% of the dishes he washes. (He, of course, will need a new job soon. . . .) You
No-shows An airline offers discounted “advance-purchase”fares to customers who buy tickets more than 30 days before travel and charges “regular” fares for tickets purchased during those last 30 days. The company has noticed that 60% of its customers take advantage of the advance-purchase
Drunks Police often set up sobriety checkpoints—roadblocks where drivers are asked a few brief questions to allow the officer to judge whether or not the person may have been drinking. If the officer does not suspect a problem, drivers are released to go on their way. Otherwise, drivers are
E-readers II Given the e-reader data presented in Exercise 78:a) If a randomly selected U.S. adult has an e-reader, what is the probability that they haven’t read an e-book in the past year?b) Is it more or less likely that a randomly selected U.S. adult who does not own an e-reader would have
Absenteeism, part II At the company described in Exercise 77, what percent of the absent employees are on the night shift?
E-readers Pew Internet reported in January of 2014 that 32%of U.S. adults own at least one e-reader, and that 28% of U.S.adults read at least one e-book in the previous year (and thus, presumably, owned an e-reader). Overall, 76% of U.S. adults read at least one book (electronic or otherwise) in
Absenteeism A company’s records indicate that on any given day about 1% of their day-shift employees and 2% of the night-shift employees will miss work. Sixty percent of the employees work the day shift.a) Is absenteeism independent of shift worked? Explain.b) What percent of employees are absent
Graduation, part II What percent of students who graduate from the college in Exercise 74 attended a public high school?
Late luggage Remember Leah (Exercise 73)? Suppose you pick her up at the Denver airport, and her luggage is not there.What is the probability that Leah’s first flight was delayed?
Graduation A private college report contains these statistics:70% of incoming first-years attended public schools.75% of public school students who enroll as first-years eventually graduate.90% of other first-years eventually graduate.
Luggage Leah is flying from Boston to Denver with a connection in Chicago. The probability her first flight leaves on time is 0.15. If the flight is on time, the probability that her luggage will make the connecting flight in Chicago is 0.95, but if the first flight is delayed, the probability that
Cars A random survey of autos parked in student and staff lots at a large university classified the brands by country of origin, as seen in the table. Is country of origin independent of type of driver?Driver Student Staff Origin American 107 105 European 33 12 Asian 55 47
Gender A poll conducted by Gallup classified respondents by sex and political party, as shown in the table. Is party affiliation independent of the respondents’ sex? Explain.Democrat Republican Independent Male 32 28 34 Female 41 25 26
Politics Given the table of probabilities from Exercise 60, are party affiliation and position on immigration independent?Explain.Stronger Immigration Enforcement Favor Oppose No Opinion PartyRepublican 0.30 0.04 0.03 Democrat 0.22 0.11 0.02 Other 0.16 0.07 0.05
Men’s health again Given the table of probabilities from Exercise 59, are high blood pressure and high cholesterol independent? Explain. Cholesterol Blood Pressure High OK High 0.11 0.21 OK 0.16 0.52
Birth order, finis In Exercises 58 and 62 we looked at the birth orders and college choices of some Intro Stats students. For these students:a) Are enrolling in Agriculture and Human Ecology disjoint?Explain.b) Are enrolling in Agriculture and Human Ecology independent? Explain.c) Are being
Unsafe food Early in 2010, Consumer Reports published the results of an extensive investigation of broiler chickens purchased from food stores in 23 states. Tests for bacteria in the meat showed that 62% of the chickens were contaminated with campylobacter, 14% with salmonella, and 9% with both.a)
Benefits Fifty-six percent of all American workers have a workplace retirement plan, 68% have health insurance, and 49% have both benefits. We select a worker at random.a) What’s the probability he has neither employer-sponsored health insurance nor a retirement plan?b) What’s the probability
Eligibility A university requires its biology majors to take a course called BioResearch. The prerequisite for this course is that students must have taken either a statistics course or a computer course. By the time they are juniors, 52% of the biology majors have taken statistics, 23% have had a
Shirts The soccer team’s shirts have arrived in a big box, and people just start grabbing them, looking for the right size. The box contains 4 medium, 10 large, and 6 extra-large shirts. You want a medium for you and one for your sister. Find the probability of each event described.a) The first
Batteries A junk box in your room contains a dozen old batteries, five of which are totally dead. You start picking batteries one at a time and testing them. Find the probability of each outcome.a) The first two you choose are both good.b) At least one of the first three works.c) The first four you
Birth order, take 2 Look again at the data about birth order of Intro Stats students and their choices of colleges shown in Exercise 58.a) If we select a student at random, what’s the probability the person is an Arts and Sciences student who is a second child(or more)?b) Among the Arts and
Global survey, take 2 Look again at the table summarizing the Roper survey in Exercise 57.a) If we select a respondent at random, what’s the probability we choose a person from the United States who has done post-graduate study?b) Among the respondents who have done post-graduate study, what’s
Immigration The table shows the political affiliations of U.S.voters and their positions on supporting stronger immigration enforcement.Stronger Immigration Enforcement Favor Oppose No Opinion PartyRepublican 0.30 0.04 0.03 Democrat 0.22 0.11 0.02 Other 0.16 0.07 0.05a) What’s the probability
Health The probabilities that an adult American man has high blood pressure and/or high cholesterol are shown in the table.What’s the probability thata) a man has both conditions?b) a man has high blood pressure?c) a man with high blood pressure has high cholesterol?d) a man has high blood
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:
Global survey The marketing research organization GfK Roper conducts a yearly survey on consumer attitudes worldwide. They collect demographic information on the roughly 1500 respondents from each country that they survey. At the top of the next column is a table showing the number of people with
Red cards You shuffle a deck of cards and then start turning them over one at a time. The first one is red. So is the second. And the third. In fact, you are surprised to get 10 red cards in a row. You start thinking, “The next one is due to be black!”a) Are you correct in thinking that
9/11? On September 11, 2002, the first anniversary of the terrorist attack on the World Trade Center, the New York State Lottery’s daily number came up 9–1–1. An interesting coincidence or a cosmic sign?a) What is the probability that the winning three numbers match the date on any given
Pepsi For a sales promotion, the manufacturer places winning symbols under the caps of 10% of all Pepsi bottles.You buy a six-pack. What is the probability that you win something?
Lights You purchased a five-pack of new light bulbs that were recalled because 6% of the lights did not work. What is the probability that at least one of your lights is defective?
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 5-day work week, what is the probability that hea) gets stopped on Monday and again on
Champion bowler A certain bowler can bowl a strike 70% of the time. If the bowls are independent, what’s 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
Disjoint or independent? In Exercise 48, you calculated probabilities involving various blood types. Some of your answers depended on the assumption that the outcomes described were disjoint; that is, they could not both happen at the same time. Other answers depended on the assumption that the
Disjoint or independent? In Exercise 47, you calculated probabilities of getting various M&M’s. Some of your answers depended on the assumption that the outcomes described were disjoint; that is, they could not both happen at the same time. Other answers depended on the assumption that the events
Blood The American Red Cross says that about 45% of the U.S. population has Type O blood, 40% Type A, 11% Type B, and the rest Type AB.a) Someone volunteers to give blood. What is the probability that this donor 1. has Type AB blood? 2. has Type A or Type B? 3. is not Type O?b) Among four potential
M&M’s The Mars company says that before the introduction of purple, yellow candies made up 20% of their plain M&M’s, red another 20%, and orange, blue, and green each made up 10%.The rest were brown.a) If you pick an M&M at random, what is the probability that 1. it is brown? 2. it is yellow or
Polling, part II According to Pew Research, the contact rate(probability of contacting a selected household) was 90% in 1997 and 62% in 2012. However, the cooperation rate (probability of someone at the contacted household agreeing to be interviewed) was 43% in 1997 and dropped to 14% in 2012.a)
Polling As mentioned in the chapter, opinion-polling organizations contact their respondents by sampling random telephone numbers. Although interviewers can reach about 62% of U.S.households, the percentage of those contacted who agree to cooperate with the survey fell from 43% in 1997 to 14% in
Final project You used the Multiplication Rule to calculate probabilities about the Calculus background of your statistics groupmates in Exercise 42.a) What must be true about the groups in order to make that approach valid?b) Do you think this assumption is reasonable? Explain.
Repairs again You used the Multiplication Rule to calculate repair probabilities for your cars in Exercise 41.a) What must be true about your cars in order to make that approach valid?b) Do you think this assumption is reasonable? Explain.
Another project You are assigned to be part of a group of three students from the Intro Stats class described in Exercise 40.What is the probability that of your other two groupmates,a) neither has studied Calculus?b) both have studied at least one semester of Calculus?c) at least one has had more
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