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intro stats
Stats Data And Models 4th Global Edition Richard D. De Veaux, Paul Velleman, David E. Bock - Solutions
Dropouts Some people are concerned that new tougher standards and high-stakes tests adopted in many states have driven up the high school dropout rate. The National Center for Education Statistics reported that the high school dropout rate for the year 2004 was 10.3%. One school district whose
Jury Census data for a certain county show that 19% of the adult residents are Hispanic. Suppose 72 people are called for jury duty and only 9 of them are Hispanic. Does this apparent underrepresentation of Hispanics call into question the fairness of the jury selection system? Explain.
Women executives A company is criticized because only 15 of 40 people in executive-level positions are women.The company explains that although this proportion is lower than it might wish, it’s not a surprising value given that only 42% of all its employees are women. What do you think? Test an
Seeds A garden center wants to store leftover packets of vegetable seeds for sale the following spring, but the center is concerned that the seeds may not germinate at the same rate a year later. The manager finds a packet of last year’s green bean seeds and plants them as a test.Although the
WebZine A magazine is considering the launch of an online edition. The magazine plans to go ahead only if it’s convinced that more than 25% of current readers would subscribe. The magazine contacted a simple random sample of 500 current subscribers, and 128 of those surveyed expressed interest.
Football 2013 During the 2013 season, the home team won 153 of the 245 regular-season National Football League games. Is this strong evidence of a home field advantage in professional football? Test an appropriate hypothesis and state your conclusion. Be sure the appropriate assumptions and
Twins A national vital statistics report indicated that about 2.5% of all births produced twins. Is the rate of twin births the same among very young mothers? Data from a large city hospital found that only 7 sets of twins were born to 423 teenage girls. Test an appropriate hypothesis and state
Scratch and dent An appliance manufacturer stockpiles washers and dryers in a large warehouse for shipment to retail stores. Sometimes in handling them the appliances get damaged. Even though the damage may be minor, the company must sell those machines at drastically reduced prices. The company
Pollution A company with a fleet of 150 cars found that the emissions systems of 2 out of the 23 they tested failed to meet pollution control guidelines. Is this strong evidence that more than 25% of the fleet might be out of compliance? Test an appropriate hypothesis and state your conclusion. Be
Med school 2013 According to the Association of American Medical Colleges, only 42% of medical school applicants were admitted to a medical school in the fall of 2013.6 Upon hearing this, the trustees of Striving College expressed concern that only 34 of the 81 students in their class of 2013 who
Law school 2011 According to the Law School Admission Council, in the fall of 2011, 71% of law school applicants were accepted to some law school.5 The training program LSATisfaction claims that 174 of the 240 students trained in 2011 were admitted to law school. You can safely consider these
Take the offer, part II In Exercise 24 of Chapter 8, you learned that First USA, a major credit card company, is planning a new offer for their current cardholders. First USA will give double airline miles on purchases for the next 6 months if the cardholder goes online and registers for this
Contributions, please, part II In Exercise 23 of Chapter 8, you learned that 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
Educated mothers The National Center for Education Statistics monitors many aspects of elementary and secondary education nationwide. Their 1996 numbers are often used as a baseline to assess changes. In 1996, 31% of students reported that their mothers had graduated from college. In 2000,
Absentees The National Center for Education Statistics monitors many aspects of elementary and secondary education nationwide. Their 1996 numbers are often used as a baseline to assess changes. In 1996, 34% of students had not been absent from school even once during the previous month. In the 2000
Abnormalities In the 1980s, it was generally believed that congenital abnormalities affected about 5% of the nation’s children. Some people believe that the increase in the number of chemicals in the environment has led to an increase in the incidence of abnormalities. A recent study examined 384
Dowsing In a rural area, only about 16% of the wells that are drilled find adequate water at a depth of 100 feet or less. A local man claims to be able to find water by“dowsing”—using a forked stick to indicate where the well should be drilled. You check with 66 of his customers and find that
Obesity 2008 In 2008, the Centers for Disease Control and Prevention reported that 34% of adults in the United States are obese. A county health service planning a new awareness campaign polls a random sample of 750 adults living there. In this sample, 228 people were found to be obese based on
Smartphones Many people have trouble setting up all the features of their smartphones, so a company has developed what it hopes will be easier instructions. The goal is to have at least 96% of customers succeed. The company tests the new system on 200 people, of whom 188 were successful. Is this
Candy Someone hands you a box with 29 chocolatecovered candies, telling you that 13 are vanilla creams and the rest are peanut butter. You pick candies at random and discover the first three you eat are all vanilla.a) If there really were 13 vanilla and 16 peanut butter candies in the box, what is
He cheats? A friend of yours claims that when he tosses a coin he can control the outcome. You are skeptical and want him to prove it. He tosses the coin, and you call heads; it’s tails. You try again and lose again.a) Do two losses in a row convince you that he really can control the toss?
Cars A survey investigating whether the proportion of today’s high school seniors who own their own cars is higher than it was a decade ago finds a P-value of 0.017.Is it reasonable to conclude that more high schoolers have cars? Explain.
Relief A company’s old antacid formula provided relief for 83% of the people who used it. The company tests a new formula to see if it is better and gets a P-value of 0.441. Is it reasonable to conclude that the new formula and the old one are equally effective? Explain.
Dice The seller of a loaded die claims that it will favor the outcome 6. We don’t believe that claim, and roll the die 200 times to test an appropriate hypothesis. Our P-value turns out to be 0.03. Which conclusion is appropriate?Explain.a) There’s a 3% chance that the die is fair.b) There’s
Positives After the political ad campaign described in Exercise 11, parta, pollsters check the president’s positives.They test the hypothesis that the ads produced no change against the alternative that the positives are now above 65% and find a P-value of 0.204. Which conclusion is appropriate?
More hypotheses Write the null and alternative hypotheses you would use to test each situation.a) In the 1950s, only about 40% of high school graduates went on to college. Has the percentage changed?b) Twenty percent of cars of a certain model have needed costly transmission work after being driven
Hypotheses Write the null and alternative hypotheses you would use to test each of the following situations:a) A president is concerned about his “positives”—the percentage of the country’s residents who express approval of his job performance. His political committee pays for a series of
Expensive medicine Developing a new drug can be an expensive process, resulting in high costs to patients. A pharmaceutical company has developed a new drug to reduce cholesterol, and it will conduct a clinical trial to compare the effectiveness to the most widely used current treatment. The
Bad medicine Occasionally, a report comes out that a drug that cures some disease turns out to have a nasty side effect. For example, some antidepressant drugs may cause suicidal thoughts in younger patients. A researcher wants to study such a drug and look for evidence that such side effects
Hispanic origin II The county supervisor in Exercise 5 is going to perform a hypothesis test to see if she has evidence that the proportion of people in her county that are of Hispanic or Latino origin is different from that for the nation. Should her alternative hypothesis be one-sided or
Psychic again (you should have seen this coming) If you were to do a hypothesis test on your experiment with your“psychic” friend from Exercise 2, would your alternative hypothesis be one-sided or two-sided? Explain wh
Empty houses According to the 2010 Census, 11.4%of all housing units in the United States were vacant.A county supervisor wonders if her county is different from this. She randomly selects 850 housing units in her county and finds that 129 of the housing units are vacant.a) State the hypotheses.b)
Hispanic origin According to the 2010 Census, 16% of the people in the United States are of Hispanic or Latino origin. One county supervisor believes her county has a different proportion of Hispanic people than the nation as a whole. She looks at their most recent survey data, which was a random
Psychic after all? The “psychic” friend from Exercise 2 correctly identified more than 25% of the cards.a) A hypothesis test gave a P-value of 0.014. What do you conclude?b) What would you conclude if the P-value had been 0.245?
Better than aspirin 2? A clinical trial compares the new drug described in Exercise 1 to aspirin. The group using the new drug had somewhat fewer heart attacks than those in the aspirin group.a) The P-value from the hypothesis test was 0.28. What do you conclude?b) What would you have concluded if
Psychic A friend of yours claims to be psychic. You are skeptical. To test this you take a stack of 100 playing cards and have your friend try to identify the suit (hearts, diamonds, clubs, or spades), without looking, of course!a) State the null hypothesis for your experiment.b) State the
Better than aspirin? A very large study showed that aspirin reduced the rate of first heart attacks by 44%.A pharmaceutical company thinks they have a drug that will be more effective than aspirin, and plans to do a randomized clinical trial to test the new drug.a) What is the null hypothesis the
Anyone who plays or watches sports has heard of the “home field advantage.”Tournaments in many sports are designed to try to neutralize the advantage of the home team or player. Most people believe that teams tend to win more often when they play at home. But do they?If there were no home field
A large city’s DMV claimed that 80% of candidates pass driving tests. Data from a reporter’s survey of randomly selected local teens who had taken the test produced a P-value of 0.002.Question: What can the reporter conclude? And how might the reporter explain what the P-value means for the
A large city’s Department of Motor Vehicles claimed that 80% of candidates pass driving tests, but a newspaper reporter’s survey of 90 randomly selected local teens who had taken the test found only 61 who passed.Question: Does this finding suggest that the passing rate for teenagers is lower
Amendment A TV news reporter says that a proposed constitutional amendment is likely to win approval in the upcoming election because a poll of 1505 likely voters indicated that 52% would vote in favor. The reporter goes on to say that the margin of error for this poll was 3%.a) Explain why the
Approval rating A newspaper reports that the governor’s approval rating stands at 60%. The article adds that the poll is based on a random sample of 1775 adults and has a margin of error of 3%. What level of confidence did the pollsters use?
Another pilot study During routine screening, a doctor notices that 22% of her adult patients show higher than normal levels of glucose in their blood—a possible warning signal for diabetes. Hearing this, some medical researchers decide to conduct a large-scale study, hoping to estimate the
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 2% and 99% confidence. To gauge the size of the problem, the agency first
Better hiring info Editors of the business report in Exercise 38 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 37, 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%?
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
Graduation It’s believed that as many as 21% 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 10% with 90%
Back to campus III Suppose ACT, Inc. wants to update their information from Exercise 34 on the percentage of freshmen that return for a second year of college.a) They want to cut the stated margin of error in half.How many college freshmen must be surveyed?b) Do you have any concerns about this
Deer ticks Wildlife biologists inspect 157 deer taken by hunters and find 33 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, again ACT, Inc. reported that 74% of 1644 randomly selected college freshmen 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
Privacy or Security? In January 2014 AP-GfK polled 1060 U.S. adults to find if people were more concerned with privacy or security. Privacy concerns outweighed concerns about being safe from terrorists for 646 out the 1060 polled. Of the 1060 adults about 180 are 65 and older whose concerns may be
Teachers A 2011 Gallup poll found that 76% of Americans believe that high achieving high school students should be recruited to become teachers. This poll was based on a random sample of 1002 Americans.a) Find a 90% confidence interval for the proportion of Americans who would agree with this.b)
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 the survey on the death penalty you read about in the chapter, the Gallup Poll actually split the sample at random, asking 510 respondents the question quoted earlier, “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 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 1160 people
Teenage drivers An insurance company checks police records on 567 accidents selected at random and notes that teenagers were at the wheel in 86 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
Still lying about age The Pew Research poll described in Exercise 1 found that 49% of a sample of 799 teens admitted to misrepresenting their age online to access websites and online services. (Treat this as a simple random sample.)a) Find the margin of error for this poll if we want 95%confidence
Baseball fans In a poll taken in December 2012, Gallup asked 1006 national adults whether they were baseball fans; 48% said they were. Three 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 The December 2011 Consumer Reports study described in Exercise 19 also found that 12 of the 22 “red snapper” packages tested were a different kind of fish.a) Are the conditions for creating a confidence interval satisfied? Explain.b) Construct a 95% confidence
Mislabeled seafood In December 2011, Consumer Reports published their study of labeling of seafood sold in New York, New Jersey, and Connecticut. They purchased 190 pieces of seafood from various kinds of food stores and restaurants in the three states and genetically compared the pieces to
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 is 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 95.00% confidence, 0.32797941 6 p(japan) 6 0.50820747
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 larger margin of error.b) For a specified
More conclusions In January 2002, 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
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 85% { 5%. 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 167
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 8%.” Explain carefully what that means.
More single moms In Exercise 4, we saw that 4% of people think the trend of more single women having children is a “good thing.”a) Are the conditions for constructing a confidence interval met?b) How many people would need to be surveyed for a 95% confidence interval to ensure the margin of
Wrong direction again Consider the St. Norbert’s College poll of Exercise 5.a) Are the assumptions and conditions met?b) How many people would need to be surveyed for a 90% confidence interval to ensure the margin of error would be less than 2%?
I asked, “How’s life?” In the Gallup poll described in Exercise 2, 49% of those polled considered themselves to be “thriving.”a) Calculate the margin of error for the proportion of all American adults who were rated as “thriving” for 99% confidence.b) Would the margin of error be
Wrong direction St. Norbert’s College in Green Bay, Wisconsin, and Wisconsin Public Radio conduct an annual poll of Wisconsinites about political opinions.The Fall 2011 survey asked a random sample of 402 adult Wisconsin residents whether they think things in the country are going in the right
Single moms In a 2010 Pew Research study on trends in marriage and family, 4% of randomly selected respondents said that the trend of more single women having children is “a good thing.” The 95% confidence interval is from 2.9% to 5.1% (n = 1229).a) Interpret this interval in this context.b)
Lying about age again The 95% confidence interval for the number of teens in Exercise 1 who reported that they had misrepresented their age online is from 45.6%to 52.5%.a) Interpret the interval in this context.b) Explain the meaning of “95% confident” in this context.
How’s life? Gallup regularly conducts a poll asking people 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 classified as“Thriving” (standing on
Lying about age Pew Research, in November 2011, polled a random sample of 799 U.S. teens about Internet use. 49%of those teens reported that they had misrepresented their age online to gain access to websites and online services.a) Explain the meaning of pn = 0.49 in the context of this
A credit card company is about to send out a mailing to test the market for a new credit card. From that sample, they want to estimate the true proportion of people who will sign up for the card nationwide. A pilot study suggests that about 0.5%of the people receiving the offer will accept
The Yale/George Mason poll that estimated that 40% of all voters believed that scientists disagree about whether global warming exists had a margin of error of {3%. Suppose an environmental group planning a follow-up survey of voters’opinions on global warming wants to determine a 95% confidence
An April 2011 Yale/George Mason poll of 1010 U.S. adults asking questions about current topics reported a margin of error of 3% It is a convention among pollsters to use a 95% confidence level and to report the “worst case” margin of error, based on p = 0.5.Question: How did the researchers
In April and May 2011, the Yale Project on Climate Change Communication and the George Mason University Center for Climate Change Communication interviewed 1010 U.S. adults about American’s global warming beliefs and attitudes.6 Question: It is standard among pollsters to use a 95% confidence
Milk Although most of us buy milk by the quart or gallon, farmers measure daily production in pounds.Ayrshire cows average 55 pounds of milk a day, with a standard deviation of 6 pounds. For Jersey cows, the mean daily production is 52 pounds, with a standard deviation of 5 pounds. Assume that
IQs Suppose that IQs of East State University’s students can be described by a Normal model with mean 130 and standard deviation 8 points. Also suppose that IQs of students from West State University can be described by a Normal model with mean 120 and standard deviation 10.a) We select a student
Potato chips The weight of potato chips in a mediumsize bag is stated to be 16 ounces. The amount that the packaging machine puts in these bags is believed to have a Normal model with mean 16.2 ounces and standard deviation 0.12 ounces.a) What fraction of all bags sold are underweight?b) Some of
Fuel economy The combined gas mileage of midsize cars varies with mean 24 miles per gallon (mpg) and a standard deviation of about 5.5 mpg. A particular rental car agency typically has 150 midsize cars in its lot. Let y represent the mean combined gas mileage for all cars in the lot.a) What’s the
Joining the museum One of the phone volunteers for the museum in exercise 56 sets a personal goal of getting an average donation of at least $100 from the new members she enrolls during the membership drive. If she gets 80 new members and they can be considered a random sample of all the museum’s
AP Stats 2013, again An AP Statistics teacher had 43 students preparing to take the AP exam discussed in Exercise 55. Though they were obviously not a random sample, he considered his students to be “typical” of all the national students. What’s the probability that his students will achieve
Museum membership A museum offers several levels of membership, as shown in the table.a) Find the mean and standard deviation of the donations.b) During their annual membership drive, they hope to sign up 50 new members each day. Would you expect the distribution of the donations for a day to
AP Stats 2013 The College Board reported the score distribution shown in the table for all students who took the 2013 AP Statistics exam.a) Find the mean and standard deviation of the scores.b) If we select a random sample of 40 AP Statistics students, would you expect their scores to follow a
New game You pay $10 and roll a die. If you get a 6, you win $50. If not, you get to roll again. If you get a 6 this time, you get your $10 back.a) Create a probability model for this game.b) Find the expected value and standard deviation of your prospective winnings.c) You play this game five
Dice and dollars You roll a die, winning nothing if the number of spots is odd, $7 for a 2 or a 4, and $16 for a 6.a) Find the expected value and standard deviation of your prospective winnings.b) You play twice. Find the mean and standard deviation of your total winnings.c) You play 40 times.
At work Some business analysts estimate that the length of time people work at a job has a mean of 6.2 years and a standard deviation of 4.5 years.a) Explain why you suspect this distribution may be skewed to the right.b) Explain why you could estimate the probability that 100 people selected at
Pregnant again The duration of human pregnancies may not actually follow the Normal model described in Exercise 49.a) Explain why it may be somewhat skewed to the left.b) If the correct model is in fact skewed, does that change your answers to partsa, b, and c of Exercise 49?Explain why or why not
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