Question: A random poll of 800 working men

> It’s common folk wisdom that cranberries can help prevent urinary tract infections in women. A leading producer of cranberry juice would like to use this information in their next ad campaign, so they need evidence of this claim. In 2001, the British Med

> Consumer Reports uses surveys given to subscribers of its magazine and website (www.ConsumerReports.org) to measure reliability in automobiles. This annual survey asks about problems that consumers have had with their cars, vans, SUVs, or trucks during t

> Students in an Introductory statistics class at a large university were classified by birth order and by the college they attend. a) What kind of chi-square test is appropriate—goodnessof- fit, homogeneity, or independence? b) State y

> The table shows the rank attained by male and female officers in the New York City Police Department (NYPD). Do these data indicate that men and women are equitably represented at all levels of the department? (All possible ranks in the NYPD are shown.)

> Here is a table showing who survived the sinking of the Titanic based on whether they were crew members or passengers booked in first-, second-, or third-class staterooms. a) If we draw an individual at random from this table, what’s

> Census data for New York City indicate that 29.2% of the under-18 population is white, 28.2% black, 31.5% Latino, 9.1% Asian, and 2% are of other ethnicities. The New York Civil Liberties Union points out that of 26,181 police officers, 64.8% are white,

> For a lottery to be successful, the public must have confidence in its fairness. One of the lotteries in Maryland is Pick-3 Lottery, where 3 random digits are drawn each day.7 A fair game depends on every value (0 to 9) being equally likely at each of th

> A sales representative who is on the road visiting clients thinks that, on average, he drives the same distance each day of the week. He keeps track of his mileage for several weeks and discovers that he averages 122 miles on Mondays, 203 miles on Tuesda

> Suppose you want to estimate the proportion of traditional college students on your campus who own their own car. You have no preconceived idea of what that proportion might be. a) What sample size is needed if you wish to be 95% confident that your esti

> A company advertises that its premium mixture of nuts contains 10% Brazil nuts, 20% cashews, 20% almonds, 10% hazelnuts, and that the rest are peanuts. You buy a large can and separate the various kinds of nuts. Upon weighing them, you find there are 112

> According to recent research (www .nas.org) married couples who met their spouse through an online dating service may have a different divorce rate than those who met “off line.” (“Online Mating” from Proceedings of the National Academy of Sciences of th

> After getting trounced by your little brother in a children’s game, you suspect that the die he gave you is unfair. To check, you roll it 60 times, recording the number of times each face appears. Do these results cast doubt on the die&

> The Chevy Tahoe Hybrid got a lot of attention when it first appeared. It is a relatively high-priced hybrid SUV that makes use of the latest technologies for fuel efficiency. One of the more popular hybrid SUVs on the market is the modestly priced Ford E

> In Exercises 50 and 52, we see the number of advertised brand names people recalled immediately after watching TV shows and 24 hours later. Strangely enough, it appears that they remembered more about the ads the next day. Should we conclude this is true

> In the study described in Exercise 50, the researchers also contacted the subjects again, 24 hours later, and asked them to recall the brands advertised. a) Is there a significant difference in viewers’ abilities to remember brands ad

> You are a consultant to the marketing department of a business preparing to launch an ad campaign for a new product. The company can afford to run ads during one TV show, and has decided not to sponsor a show with sexual content (see Exercise 50). You cr

> The Journal of Applied Psychology reported on a study that examined whether the content of TV shows influenced the ability of viewers to recall brand names of items featured in the commercials. The researchers randomly assigned volunteers to watch one of

> A small appliance company is interested in comparing delivery times of their product during two months. They are concerned that the summer slow-downs in August cause delivery times to lag during this month. Given the following delivery times (in days) of

> When implementing a packaged Enterprise Resource Planning (ERP) system, many companies report that the module they first install is Financial Accounting. Among the measures used to gauge the effectiveness of their ERP system implementation is acceleratio

> As in Exercise 13, from a survey of coworkers you find that 48% of 200 have already received this year’s flu vaccine. An approximate 95% confidence interval is (0.409, 0.551). a) How would the confidence interval change if the sample size had been 800 i

> A company institutes an exercise break for its workers to see if this will improve job satisfaction, as measured by a questionnaire that was given to a random sample of workers to assess their satisfaction. a) Identify the procedure you would use to a

> The Price-to-Book-value ratio is often used by investors to indicate whether a stock’s price is particularly high or low relative to the value of the company. But different market sectors expect different Price/Book values. Here are dat

> In an investigation of environmental causes of disease, data were collected on the annual mortality rate (deaths per 100,000) for males in 61 large towns in England and Wales. In addition, the water hardness was recorded as the calcium concentration (par

> Do the data in Exercise 42 suggest that the American League’s designated hitter rule may lead to more runs per game scored? a) Write the null and alternative hypotheses. b) Find a 95% confidence interval for the difference in mean runs per game, and inte

> A factory hiring people to work on an assembly line gives job applicants a test of manual agility. a) Find 95% confidence intervals for the average number of pegs that males and females can each place. b) Those intervals overlap. What does this suggest

> American League baseball teams play their games with the designated hitter rule, meaning that pitchers do not bat. The league believes that replacing the pitcher, traditionally a weak hitter, with another player in the batting order produces more runs an

> A pharmaceutical company is producing and marketing a ginkgo biloba supplement to enhance memory. In an experiment to test the product, subjects were assigned randomly to take ginkgo biloba supplements or a placebo. Their memory was tested to see whether

> Exercise 39 considered possible changes in the numbers of tropical cyclones that have grown large enough to be officially named. Regardless of the number of storms, has the fraction of named storms that grew to hurricane strength changed? Here are those

> It has been suggested that global climate change may be affecting the frequency of tropical storms. The data here show the number of tropical cyclones (including hurricanes) assigned official names by the National Hurricane Center. Is there evidence of a

> The owner of a small organic food store was concerned about her sales of a specialty yogurt manufactured in Greece. As a result of increasing fuel costs, she recently had to increase its price. To help boost sales, she decided to place the product on a d

> From the survey in Exercise 11, a) How would the confidence interval change if the confidence level had been 90% instead of 95%? b) How would the confidence interval change if the sample size had been 300 instead of 200? (Assume the same sample proport

> A company is producing and marketing new reading activities for elementary school children that it believes will improve reading comprehension scores. A researcher randomly assigns third graders to an eight-week program in which some will use these activ

> The Pew Internet & American Life Project (www.pewinternet.org/) conducts surveys to gauge how the Internet and technology impact daily life of individuals, families, and communities. In a recent survey Pew asked respondents if they thought that compu

> Morningstar (www.morningstar.com) selects mutual funds as “Medalist” funds expected to perform well over the long term. You have decided to invest in a bond fund and plan to limit your choice of funds to Morningstar “medalist” funds. But now you must cho

> Chemical analyses of 1599 red and 4898 white Italian wines revealed the following summary statistics for pH (a measure of acidity): Is there a difference in pH between red and white wines? a) Write the null and alternative hypotheses. b) What condition

> A food company is concerned about recent criticism of the sugar content of their children’s cereals. The data show the sugar content (as a percentage of weight) of several national brands of children’s and adults&acirc

> Suppose the specialty food chain from Exercise 26 wants to now compare the change in sales across different regions. An examination of the difference in sales over a 37-week period in a recent year for 8 stores in the state of Massachusetts compared to 1

> A trucking company would like to compare two different routes for efficiency. Truckers are randomly assigned to two different routes. Twenty truckers following Route A report an average of 40 minutes, with a standard deviation of 3 minutes. Twenty trucke

> The accounting firm described in Exercise 28 is interested in providing opportunities for its auditors to gain more expertise in statistical sampling methods. They wish to compare traditional classroom instruction with online self-paced tutorials. Audito

> The study of the new CPMP mathematics methodology described in Exercise 25 also tested students’ abilities to solve word problems. This table shows how the CPMP and traditional groups performed. What do you conclude? (Assume that the as

> An accounting firm is trying to decide between IT training conducted in-house and the use of third party consultants. To get some preliminary cost data, each type of training was implemented at two of the firm’s offices located in diffe

> From the survey in Exercise 11, which of the following are true? If they are not true, explain briefly why not. a) 95% of the 200 students are in the interval (0.283, 0.417). b) The true proportion of students who use laptops to take notes is captured

> During the study described in Exercise 25, students in both CPMP and traditional classes took another algebra test that did not allow them to use calculators. The table shows the results. Are the mean scores of the two groups significantly different? Ass

> A chain that specializes in healthy and organic food would like to compare the sales performance of two of its primary stores in the state of Massachusetts. These stores are both in urban, residential areas with similar demographics. A comparison of the

> The Core Plus Mathematics Project (CPMP) is an innovative approach to teaching mathematics that engages students in group investigations and mathematical modeling. After field tests in 36 high schools over a three-year period, researchers compared the pe

> The Consumer Reports article described in Exercise 23 also listed the sodium content (in mg) for the various hot dogs tested. A test of the null hypothesis that beef hot dogs and meat hot dogs don’t differ in the mean amounts of sodium yields a P-value o

> Consumers increasingly make food purchases based on nutrition values. Consumer Reports examined the calorie content of two kinds of hot dogs: meat (usually a mixture of pork, turkey, and chicken) and all beef. The researchers purchased samples of several

> The manufacturer of a new sleeping pill suspects that it may increase the risk of sleepwalking, which could be dangerous. A test of the drug fails to reject the null hypothesis of no increase in sleepwalking when tested at a = 0.01. a) If the test had b

> An enthusiastic junior executive has run a test of his new marketing program. He reports that it resulted in a “significant” increase in sales. A footnote on his report explains that he used an alpha level of 7.2% for his test. Presumably, he performed a

> Yahoo surveyed 2400 U.S. men. Of the men, 1224 identified themselves as the primary grocery shopper in their household. a) Estimate the percentage of all American males who identify themselves as the primary grocery shopper. Use a 98% confidence interva

> A new program may reduce the proportion of employees who fail a computer skills course. The company that developed this program supplied materials and teacher training for a large-scale test involving nearly 8500 employees in several different sites. Sta

> From a survey of coworkers you find that 48% of 200 have already received this year’s flu vaccine. An approximate 95% confidence interval is (0.409, 0.551). Which of the following are true? If not, explain briefly. a) 95% of the coworkers fall in the in

> Health researchers at a large HMO base their cost predictions for measles on the belief that 98% of children have been vaccinated against measles. A random survey of medical records at many schools across the country found that, among more than 13,000 ch

> Analysts evaluating a new program to encourage customer retention in a test market find no evidence of an increased rate of retention in a test of 2000 customers. They based this conclusion on a test using a = 0.01. Would they have made the same decision

> A researcher developing scanners to search for hidden weapons at airports has concluded that a new device is significantly better than the current scanner. He made this decision based on a test using a = 0.05. Would he have made the same decision at a =

> An automatic character recognition device can successfully read about 85% of handwritten loan 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 1

> When they send out their fundraising letter, 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

> A philanthropic organization knows that its donors have an average age near 60 and is considering taking out an ad in the American Association of Retired People (AARP) magazine. An analyst wonders what proportion of their donors are actually 50 years old

> The data set provided contains credit card purchases of 500 customers in the month before Christmas, randomly chosen from a segment of a major credit card issuer. The marketing department is considering a special offer for customers who spend more than $

> The Board of Directors of a publicly traded company says that a proposed amendment to their bylaws is likely to win approval in the upcoming election because a poll of 1505 stock owners indicated that 52% would vote in favor. The Board goes on to say tha

> A newspaper reports that the governor’s approval rating stands at 65%. The article adds that the poll is based on a random sample of 972 adults and has a margin of error of 2.5%. What level of confidence did the pollsters use?

> During routine conversations, the CEO of a new start-up reports that 22% of adults between the ages of 21 and 39 will purchase her new product. Hearing this, some investors decide to conduct a large-scale study, hoping to estimate the proportion to withi

> 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