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 goal is to keep the level of damaged machines below 2%. One day an inspector randomly checks 60 washers and finds that 5 of them have scratches or dents. Is this strong evidence that the warehouse is failing to meet the company goal? Test an appropriate hypothesis and state your conclusion. Be sure the appropriate assumptions and conditions are satisfied before you proceed.
> 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
> According to the U.S. Census Bureau (www.census.gov/housing/hvs/files/currenthvspress.pdf), in 2017, 63.9% of American families owned their homes. Census data reveal that the ownership rate in one small city is even lower. The city council is debating a
> 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
> 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
> During the week of April 15, 2013, a Gallup Poll asked 1500 U.S. adults, aged 18 or over, how they rated economic conditions. Only 17% rated the economy as Excellent/Good. Construct a 95% confidence interval for the true proportion of Americans who rated
> In a survey on downloading music, the Gallup Poll asked 703 Internet users if they “ever downloaded music from an Internet site that was not authorized by a record company, or not,” and 18% responded “yes.” Construct a 95% confidence interval for the tru
> 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 sh
> 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 surv
> Direct mail advertisers send solicitations (“junk mail”) to thousands of potential customers in the hope that some will buy the company’s product. The response rate is usually quite low. Suppose a company wants to test the response to a new f lyer and se
> 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) Expla
> A biotechnology firm in Boston is planning its investment strategy for future products and research labs. A poll found that only 8% of a random sample of 1012 U.S. adults approved of attempts to clone a human. a) Find the margin of error for this poll i
> A small company involved in e-commerce is interested in statistics concerning the use of e-mail. A poll found that 38% of a random sample of 1012 adults, who use a computer at their home, work, or school, said that they do not send or receive e-mail. a)
> For quality control purposes, 900 ceramic tiles were inspected to determine the proportion of defective (e.g., cracked, uneven finish, etc.) tiles. Assuming that these tiles are representative of all tiles manufactured by an Italian tile company, what ca
> Look back at the prices for the external disk drives we saw in Exercise 10. The least squares line is The assumptions and conditions for regression are met. a) Disk drives keep growing in capacity. Some tech experts now talk about Petabyte 1PB = 100
> A student is considering publishing a new magazine aimed directly at owners of Japanese automobiles. He wanted to estimate the fraction of cars in the United States that are made in Japan. The computer output summarizes the results of a random sample of
> How far do professional golfers drive a ball? (For non-golfers, the drive is the shot hit from a tee at the start of a hole and is typically the longest shot.) Here’s a histogram of the average driving distances of the 199 leading profe
> 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 for inference. b) Create a 95% confidence interval for the averag
> After the sub-prime crisis of late 2007, real estate prices fell almost everywhere in the United States. In 2006–2007 before the crisis, the average selling price of homes in a region in upstate New York was $191,300. A real estate agen
> Should you generate electricity with your own personal wind turbine? That depends on whether you have enough wind on your site. To produce enough energy, your site should have an annual average wind speed of at least 8 miles per hour, according to the Wi
> While reviewing the sample of audit fees, a senior accountant for the firm notes that the fee charged by the firm’s accountants depends on the complexity of the return. A comparison of actual charges therefore might not provide the information needed to
> 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 speed-measuring machines must measure accurately to maximize effectiveness in slowing traffic. The accuracy of the machines will be tested before placement on city streets. To ensure that error rates are estimated accurately, the researchers want to
> Police departments often try to control traffic speed by placing speed-measuring machines on roads that tell motorists how fast they are driving. Traffic safety experts must determine where machines should be placed. In one recent test, police recorded t
> At one time, Nevada was the only U.S. state that allowed gambling. Although gambling continues to be one of the major industries in Nevada, the proliferation of legalized gambling in other areas of the country has required state and local governments to
> Recall the small bookstore we saw in Exercise 9. The regression line is: and the assumptions and conditions for regression are met. Calculations with technology find that se = 1.477. a) Find the predicted sales on a day with 500 employees working. b)
> Government officials have difficulty attracting new business to communities with troubled reputations. Nevada has been one of the fastest growing states in the country for a number of years. Accompanying the rapid growth are massive new construction proj
> A company that produces cell phones claims its standard phone battery lasts longer on average than other batteries in the market. To support this claim, the company publishes an ad reporting the results of a recent experiment showing that under normal us
> The technology committee has stated that the average time spent by students per lab visit has increased, and the increase supports the need for increased lab fees. To substantiate this claim, the committee randomly samples 12 student lab visits and notes
> Will your flight get you to your destination on time? The U.S. Bureau of Transportation Statistics reported the percentage of f lights that were late each month from 1995 through early 2016. Here’s a histogram, along with some summary s
> What are the chances your f light will leave on time? The U.S. Bureau of Transportation Statistics of the Department of Transportation publishes information about airline performance. Here are a histogram and summary statistics for the percentage of f li
> Suppose the state in Exercise 33 sampled 16 small retailers instead of 51, and for the sample of 16, the sample mean increase again equaled $2350 in additional sales tax revenue collected per retailer compared to the previous quarter. Also assume the sam
> States that rely on sales tax for revenue to fund education, public safety, and other programs often end up with budget surpluses during economic growth periods (when people spend more on consumer goods) and budget deficits during recessions (when people
> In Exercise 30, we found a 95% confidence interval to estimate the average value of foreclosed homes. a) Suppose the standard deviation of the values was $300,000 instead of the $196,196 used for that interval. What would the larger standard deviation d
> Suppose that for budget planning purposes the city in Exercise 29 needs a better estimate of the mean daily income from parking fees. a) Someone suggests that the city use its data to create a 95% confidence interval instead of the 90% interval first cr
> In 2012, a large number of foreclosed homes in the Washington, DC, metro area were sold. In one community, a sample of 30 foreclosed homes sold for an average of $443,705 with a standard deviation of $196,196. a) What assumptions and conditions must be c
> In Exercise 5, we saw a regression to predict the sales per person at a movie theater in terms of the time (in minutes) before the show. The model was: a) A 90% prediction interval for sales to a concessions customer 10 minutes before the movie starts
