Question: According to the U.S. Census Bureau (

> From a survey of 250 coworkers you find that 155 would like the company to provide on-site day care. a) What is the value of the sample proportion pn? b) What is the standard error of the sample proportion? c) Construct an approximate 95% confidence i

> A state’s environmental agency worries that a large percentage of 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

> 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?

> 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%?

> The research group that conducted the survey in Exercise 70 wants to provide the music industry with definitive information, but they believe that they could use a smaller sample next time. If the group is willing to have twice as big a margin of error,

> A company manufacturing CDs is working on a new technology. A random sample of 703 Internet users were asked: “As you may know, some CDs are being manufactured so that you can only make one copy of the CD after you purchase it. Would you buy a CD with th

> A random sample of 168 students was asked how many songs were in their digital music library and what fraction of them was legally purchased. Overall, they reported having a total of 117,079 songs, of which 23.1% were legal. The music industry would like

> A recent poll of 1005 U.S. adults split the sample into four age groups: ages 18–29, 30–49, 50–64, and 65+. In the youngest age group, 62% said that they thought the United States was ready for a woman president, as opposed to 35% who said, “no, the coun

> A Gallup Poll (Exercise 57) asked Americans if the fact that they can make copies of songs on the Internet for free made them more likely—or less likely—to buy a performer’s CD. Only 13% responded that it made them “less likely.” The poll was based on a

> In a random survey of 226 self-employed individuals, 20 reported having had their tax returns audited by the IRS in the past year. Estimate the proportion of self-employed individuals nationwide who’ve been audited by the IRS in the past year. a) Check

> A telemarketer at a credit card company is instructed to ask the next 18 customers that call into the 800 number whether they are aware of the new Platinum card that the company is offering. Of the 18, 17 said they were aware of the program. a) Check th

> A survey of 200 students is selected randomly on a large university campus. They are asked if they use a laptop in class to take notes. The result of the survey is that 70 of the 200 students responded “yes.” a) What is the value of the sample proportion

> A paralegal at the Vermont State Attorney General’s office wants to know how many companies in Vermont provide health insurance benefits to all employees. She chooses 12 companies at random and finds that all 12 offer benefits. a) Check the assumptions

> A real estate agent looks over the 15 listings she has in a particular ZIP code in California and finds that 80% of them have swimming pools. a) Check the assumptions and conditions for inference on proportions. b) If it’s appropriate, find a 90% confi

> In 2012, Gallup published a report entitled “Qatar’s Rising Entrepreneurial Spirit” in which they concluded that the 33% of 1057 Qatari youth they surveyed who responded that they plan to start their own business was the highest in the region. They condu

> In a survey on corporate ethics, a poll split a sample at random, asking 538 faculty and corporate recruiters the question: “Generally speaking, do you believe that MBAs are more or less aware of ethical issues in business today than five years ago?” The

> GfK Roper surveyed people worldwide, asking them, “How important is acquiring wealth to you?” Of 1535 respondents in India, 1168 said that it was of more than average importance. In the United States, of 1317 respondents, 596 said it was of more than ave

> In Canada, the vast majority (90%) of companies in the chemical industry are ISO 14001 certified. The ISO 14001 is an international standard for environmental management systems. An environmental group wished to estimate the percentage of U.S. chemical c

> A bootstrap test of the hypothesis in Exercise 56 produced the following distribution (shifted to center the histogram at the hypothesized mean of 649): (Data in Student survey) a) What is the P-value of this test? b) Write a sentence or two with your

> A student resampled the Maze times from Exercise 55 1000 times. The histogram shows the distributions of the means, and a summary of the quantiles is shown below it. a) Find a 99% bootstrap confidence interval for the true mean time it takes to comple

> According to www.marketingcharts.com/, the average 18–24-year old has 649 Facebook friends. The student who collected the survey data in Student survey wanted to test if the mean number is higher at his school. Using his data, test an appropriate hypothe

> A new operating system is installed in every workstation at a large company. The claim of the operating system manufacturer is that the time to shut down and turn on the machine will be much faster. To test it an employee selects 36 machines and tests th

> Here are the data from the researcher studying the reaction times of rats. He has a requirement that the maze take about a minute to complete on average. a) Plot the data. Do you think the conditions are satisfied? Explain. b) Do you think this maze mee

> As we saw in Chapter 11, Exercise 51, Consumer Reports tested 11 brands of vanilla yogurt and found these numbers of calories per serving: 130 160 150 120 120 110 170 160 110 130 90 a) Check the assumptions and conditions. b) A diet guide claims that y

> In 1998, in a famous advertising campaign, the Nabisco Company announced a “1000 Chips Challenge,” claiming that every 18-ounce bag of their Chips Ahoy! cookies contained at least 1000 chocolate chips. Dedicated statis

> Pop’s Popcorn, Inc., needs to determine the optimum power and time settings for their new licoricef lavored microwave popcorn. They want to find a combination of power and time that delivers high-quality popcorn with less than 10% of the kernels left unp

> SLIX wax is developing a new high performance f luorocarbon wax for cross country ski racing designed to be used under a wide variety of conditions. In order to justify the price marketing wants, the wax needs to be very fast. Specifically, the mean time

> The philanthropic organization of Exercise 42 decided to go ahead with the new gift. In mailings to 98,000 prospects, the new mailing yielded an average of $0.78. If they had decided based on their initial trial not to use this gift, what kind of error w

> The owner of the collection agency in Exercise 41 is quite certain that they can collect more than $200 per customer on average. He urges that the credit card company run a larger trial. Do you think a larger trial might help the company make a better de

> You are in charge of shipping computers to customers. You learn that a faulty RAM chip was put into some of the machines. There’s a simple test you can perform, but it’s not perfect. All but 4% of the time, a good chip passes the test, but unfortunately,

> In a drawer are two coins. They look the same, but one coin produces heads 90% of the time when spun while the other one produces heads only 30% of the time. You select one of the coins. You are allowed to spin it once and then must decide whether the co

> The catheter company in Exercise 44 is reviewing its testing procedure. a) Suppose the significance level is changed to a = 0.01. Will the probability of a Type II error increase, decrease, or remain the same? b) What is meant by the power of the test

> In order to judge whether the program is successful, the manager of the supermarket chain in Exercise 19 wants to know the plausible range of values for the mean increase in customers using the program. Construct a 90% confidence interval.

> The manufacturer of the metal TV stands in Exercise 43 is thinking of revising its safety test. a) If the company’s lawyers are worried about being sued for selling an unsafe product, should they increase or decrease the value of a? Explain. b) In this

> During an angiogram, heart problems can be examined via a small tube (a catheter) threaded into the heart from a vein in the patient’s leg. It’s important that the company that manufactures the catheter maintain a diameter of 2.00 mm. (The standard devia

> The manufacturer of a metal stand for home TV sets must be sure that its product will not fail under the weight of the TV. Since some larger sets weigh nearly 300 pounds, the company’s safety inspectors have set a standard of ensuring that the stands can

> A philanthropic organization sends out “free gifts” to people on their mailing list in the hope that the receiver will respond by sending back a donation. Typical gifts are mailing labels, greeting cards, or post cards. They want to test out a new gift t

> Credit card companies lose money on cardholders who fail to pay their minimum payments. They use a variety of methods to encourage their delinquent cardholders to pay their credit card balances, such as letters, phone calls, and eventually the hiring of

> 203 students signed up for the Stats course in Exercise 39. They used the software suggested by the salesman, and scored an average of 108 points on the final with a standard deviation of 8.7 points. a) Should the professor spend the money for this soft

> A statistics professor has observed that for several years students score an average of 105 points out of 150 on the semester exam. A salesman suggests that he try a statistics software package that gets students more involved with computers, predicting

> Highway safety engineers test new road signs, hoping that increased ref lectivity will make them more visible to drivers. Volunteers drive through a test course with several of the new- and old-style signs and rate which kind shows up the best. a) Is th

> A company is sued for job discrimination because only 19% of the newly hired candidates were minorities when 27% of all applicants were minorities. Is this strong evidence that the company’s hiring practices are discriminatory? a) Is this a one-tailed o

> Consider again the task of the quality control inspectors in Exercise 34. a) In this context, what is meant by the power of the test the inspectors conduct? b) They are currently testing 5 items each hour. Someone has proposed that they test 10 instead

> A city wants to know if a new advertising campaign to make citizens aware of the dangers of driving after drinking has been effective. They count the number of drivers who have been stopped with more alcohol in their systems than the law allows for each

> A training center, wishing to demonstrate the effectiveness of their methods, tests some of their clients after different numbers of days of training, recording their scores on a sample test. Their data are: The regression model they calculate is a)

> As in Exercise 33, state regulators are checking up on repair shops to see if they are certifying vehicles that do not meet pollution standards. a) In this context, what is meant by the power of the test the regulators are conducting? b) Will the power

> Production managers on an assembly line must monitor the output to be sure that the level of defective products remains small. They periodically inspect a random sample of the items produced. If they find a significant increase in the proportion of items

> A clean air standard requires that vehicle exhaust emissions not exceed specified limits for various pollutants. Many states require that cars be tested annually to be sure they meet these standards. Suppose state regulators double-check a random sample

> Testing for Alzheimer’s disease can be a long and expensive process, consisting of lengthy tests and medical diagnosis. A group of researchers (Solomon et al., 1998) devised a 7-minute test to serve as a quick screen for the disease for use in the genera

> Consider again the points-based spam filter described in Exercise 28. When the points assigned to various components of an e-mail exceed the cutoff value you’ve set, the filter rejects its null hypothesis (that the message is real) and diverts that e-mai

> Exercise 27 describes the loan score method a bank uses to decide which applicants it will lend money. Only if the total points awarded for various aspects of an applicant’s financial condition fail to add up to a minimum cutoff score set by the bank wil

> Spam filters try to sort your e-mails, deciding which are real messages and which are unwanted. One method used is a point system. The filter reads each incoming e-mail and assigns points to the sender, the subject, key words in the message, and so on. T

> Before lending someone money, banks must decide whether they believe the applicant will repay the loan. One strategy used is a point system. Loan officers assess information about the applicant, totaling points they award for the person’s income level, c

> The health care analyst in Exercise 18 finds a 90% confidence interval for the true proportion of employees who fail the course to be (14.46%, 15.74%). a) Explain why she can reject the null hypothesis that p = 0.159 vs. p 6 0.159 at a = 0.05. b) Expla

> A supermarket chain wants to know if their “buy one, get one free” campaign increases customer traffic enough to justify the cost of the program. For each of 10 stores they select two days at random to run the test. Fo

> The analyst in Exercise 17 finds a 98% confidence interval for the true proportion of vaccinated children to be (0.9707, 0.9773). a) Explain why she can reject the null hypothesis that p = 0.98 vs. p 6 0.98 at a = 0.01. b) Explain why the difference ma

> Zocdoc.com provides a service to find and make appointments with medical professionals across the United States. Suppose an analyst looking to see if a new web design had improved the percentage of people successfully making appointments found a z-score

> A software engineer at Neverware, a company that replaces computers in schools with terminals connected to a server, is testing a new server to see if mean download times are decreased with the new server. When he compares a random sample of 20 times to

> Bjork Larsen was trying to decide whether to use a new racing wax for cross-country skis. He decided that the wax would be worth the price if he could average less than 55 seconds on a course he knew well, so he planned to study the wax by racing on the

> Yvon Hopps ran an experiment to determine optimum power and time settings for microwave popcorn. His goal was to find a combination of power and time that would deliver high-quality popcorn with less than 10% of the kernels left unpopped, on average. Exp

> Some students checked 6 bags of Doritos marked with a net weight of 28.3 grams. They carefully weighed the contents of each bag, recording the following weights (in grams): 29.2, 28.5, 28.7, 28.9, 29.1, 29.5. (Data in Doritos) a) Do these data satisfy t

> Students investigated the packaging of potato chips. They purchased 6 bags of Lay’s Ruff les marked with a net weight of 28.3 grams. They carefully weighed the contents of each bag, recording the following weights (in grams): 29.3, 28.2, 29.1, 28.7, 28.9

> A college’s technology committee wants to perform a test to see if the mean amount of time students are spending in the computer lab has increased from 55 minutes. Here are the data from a random sample of 12 students. a) Plot the dat

> A researcher tests whether the mean cholesterol level among those who eat frozen pizza exceeds the value considered to indicate a health risk. She gets a P-value of 0.04. Explain in this context what the “4%” represents.

> A nutrition lab tested 40 hot dogs to see if their mean sodium content was less than the 325-mg upper limit set by regulations for “reduced sodium” franks. The mean sodium content for the sample was 322.0 mg with a standard deviation of 18 mg. Assume tha

> For each of the following scenarios, say whether the data should be treated as independent or paired samples. Explain briefly. If paired, explain what the pairing involves. a) An efficiency expert claims that a new ergonomic desk chair makes typing at a

> Certified public accountants are often required to appear with clients if the IRS audits the client’s tax return. Some accounting firms give the client an option to pay a fee when the tax return is completed that guarantees tax advice and support from th

> The College Board reported that 53.8% of all students who took the 2017 AP Statistics exam earned scores of 3 or higher. One teacher wondered if the performance of her school was better. She believed that year’s students to be typical of those who will t

> Like a lot of other Americans, John Wayne died of cancer. But is there more to this story? In 1955, Wayne was in Utah shooting the film The Conqueror. Across the state line, in Nevada, the United States military was testing atomic bombs. Radioactive fall

> A startup company is about to market a new computer printer. It decides to gamble by running commercials during the Super Bowl. The company hopes that name recognition will be worth the high cost of the ads. The goal of the company is that over 40% of th

> An airline’s public relations department says that the airline rarely loses passengers’ luggage. It further claims that on those occasions when luggage is lost, 90% is recovered and delivered to its owner within 24 hours. A consumer group that surveyed a

> A study of the effects of acid rain on trees in the Hopkins Forest shows that 25 of 100 trees sampled exhibited some sort of damage from acid rain. This rate seemed to be higher than the 15% quoted in a recent Environmetrics article on the average propor

> 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 (nces.ed.gov/ fastfacts/) reported that the high school dropout ra

> 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 jur

> A company is criticized because only 13 of 43 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 40% of all its employees are women. W

> 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 p

> For each of the following scenarios, say whether the data should be treated as independent or paired samples. Explain briefly. If paired, explain what the pairing involves. a) An efficiency expert claims that a new ergonomic desk chair makes typing at a

> 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 137 of t

> During the first 15 weeks of the 2016 season, the home team won 137 of the 238 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 conclu

> A national vital statistics report indicated that about 3% 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 469 teenage girls. Test an

> 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 re

> A company with a fleet of 150 cars found that the emissions systems of 7 out of the 22 they tested failed to meet pollution control guidelines. Is this strong evidence that more than 20% of the fleet might be out of compliance? Test an appropriate hypoth

> First USA tested the effectiveness of a double miles campaign by recently sending out offers to a random sample of 50,000 cardholders. Of those, 1184 registered for the promotion. Even though this is nearly a 2.4% rate, a staff member suspects that the s

> The Paralyzed Veterans of America recently sent letters to a random sample of 100,000 potential donors and received 4781 donations. They’ve had a contribution rate of 5% in past campaigns, but a staff member worries that the rate is lower now that they’v

> 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 fro

> 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 dur

> 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

> For the data in Exercise 4, a) Test the null hypothesis at a = 0.05 using the pooled t-test. (Show the t-statistic, P-value, and conclusion.) b) Find a 95% confidence interval using the pooled degrees of freedom. c) Are your answers different from wha

> In a rural area, only about 30% 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 8

> In 2016, the Centers for Disease Control and Prevention reported that 36.5% 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 w

> 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 who

> Someone hands you a box of a dozen chocolate covered candies, telling you that half are vanilla creams and the other half peanut butter. You pick candies at random and discover the first three you eat are all vanilla. a) If there really were 6 vanilla a

> 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

> 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.

> A company’s old antacid formula provided relief for 70% of the people who used it. The company tests a new formula to see if it is better and gets a P-value of 0.27. Is it reasonable to conclude that the new formula and the old one are equally effective?

> 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% ch

> After the political ad campaign described in Exercise 15, part a, pollsters check the governor’s negatives. They test the hypothesis that the ads produced no change against the alternative that the negatives are now below 30% and find a P-value of 0.22.

> 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 tra

> For the data in Exercise 3, a) Test the null hypothesis at a = 0.05 using the pooled t-test. (Show the t-statistic, P-value, and conclusion.) b) Find a 95% confidence interval using the pooled degrees of freedom. c) Are your answers different from wha

> Write the null and alternative hypotheses you would use to test each of the following situations: a) A governor is concerned about his “negatives”—the percentage of state residents who express disapproval of his job performance. His political committee