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 strong evidence that the new system fails to meet the company goal? A student test of this hypothesis is shown. How many mistakes can you find? H0:p^=0.96HA:p^‰0.96SRS, 0.96(200)>10188200=0.94;SD(p^)=(0.94)(0.06)200=0.017z=0.96 0.940.017=1.18P=P(z>1.18)=0.12
> 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 income level, cre
> A survey of 81 randomly selected people standing in line to enter a football game found that 73 of them were home team fans. a. Explain why we cannot use this information to construct a confidence interval for the proportion of all people at the game who
> Canine hip dysplasia is a degenerative disease that causes pain in many dogs. Sometimes advanced warning signs appear in puppies as young as 6 months. A veterinarian checked 42 puppies whose owners brought them to a vaccination clinic, and she found 5 wi
> In June 2010, a random poll of 800 working men found that 9% had taken on a second job to help pay the bills. (www.careerbuilder.com) 1. Estimate the true percentage of men that are taking on second jobs by constructing a 95% confidence interval. 2. A pu
> In January 2014, 16 gas stations in eastern Wisconsin posted these prices for a gallon of regular gasoline: 1. Make a stem-and-leaf display of these gas prices. Use split stems; for example, use two 3.2 stems one for prices between $3.20 and $3.24 and th
> In January 2016, at the end of his time in office, President Obama approval rating stood at 57% in Gallup daily tracking poll of 1500 randomly surveyed U.S. adults. (www.gallup.com/poll/113980/gallup-daily-obama-job-approval.aspx) 1. Make a 95% confidenc
> Soon after the euro was introduced as currency in Europe, it was widely reported that someone had spun a euro coin 250 times and gotten heads 140 times. We wish to test a hypothesis about the fairness of spinning the coin. 1. Estimate the true proportion
> Yahoo surveyed 2400 U.S. men. 1224 of the men identified themselves as the primary grocery shopper in their household. 1. Estimate the percentage of all American males who identify themselves as the primary grocery shopper. Use a 98% confidence interval.
> Environmentalists concerned about the impact of high-frequency radio transmissions on birds found that there was no evidence of a higher mortality rate among hatchlings in nests near cell towers. They based this conclusion on a test using α=0.05. Would
> 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 α=0.05. Would he have made the same decision at α=0.
> Have harsher penalties and ad campaigns increased seat-belt use among drivers and passengers? Observations of commuter traffic failed to find evidence of a significant change compared with three years ago. Explain what the study P-value of 0.17 means in
> A medical researcher tested a new treatment for poison ivy against the traditional ointment. He concluded that the new treatment is more effective. Explain what the P-value of 0.047 means in this context.
> 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 hypot
> Here are the data from the researcher studying the reaction times of rats from Chapter 17, Exercise 61. Recall that he has a requirement that the maze take about a minute to complete on average. 1. Plot the data. Do you think the conditions are satisfied
> As we saw in Chapter 17, Exercise 60, Consumer Reports tested 11 brands of vanilla yogurt and found these numbers of calories per serving: 1. Check the assumptions and conditions. 2. A diet guide claims that you will get an average of 120 calories from a
> A meteorologist preparing a talk about global warming compiled a list of weekly low temperatures (in degrees Fahrenheit) he observed at his southern Florida home last year. The coldest temperature for any week was 36°F, but he inadvertently recorded the
> As we learned in Chapter 17, Exercise 59, in 1998, as an 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 statisti
> From Chapter 17, Exercise 58, 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 s
> In Chapter 17, Exercise 57 we saw that 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
> We saw in Chapter 17, Exercise 56 that 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. 1. Do
> Recall from Chapter 17, Exercise 55 that students investigated the packaging of potato chips. They purchased 6 bags of Lay Ruffles marked with a net weight of 28.3 grams. They carefully weighed the contents of each bag, recording the following weights (i
> The technology committee of Chapter 17, Exercise 42 wants to perform a test to see if the mean amount of time students are spending in the lab has increased from 55 minutes. Here are the data from a random sample of 12 students. 1. Plot the data. Are any
> The researcher from Chapter 17, Exercise 39 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 0.07. Explain in this context what the 7% represents.
> The nutrition lab in Chapter 17, Exercise 38 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 dev
> From the measurements of body temperature in Chapter 17, Exercise 29, you created a confidence interval for the true mean body temperature of healthy adults. 1. 98.6°F is commonly assumed to be normal. Set up the null and alternative hypothese
> The College Board reported that 60.3% of all students who took the 2016 AP Statistics exam earned scores of 3 or higher. One teacher wondered if the performance of her school was better. She believed that year students to be typical of those who will tak
> The histogram shows total gross earnings (in millions of dollars) of the top 200 major release movies in 2015. (Data extracted from Movies_06-15) An industry publication reports that the typical movie makes $23.2 million, but a watchdog group concerned w
> 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 start-up 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 t
> An airline 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 la
> 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 reported that the high school dropout rate for the year 2014 was 6
> 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 not a surprising value given that only 40% of all its employees are women. Wha
> 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 green bean seeds and pla
> A magazine is considering the launch of an online edition. The magazine plans to go ahead only if it convinced that more than 25% of current readers would subscribe. The magazine contacted a Simple Random Sample of 500 current subscribers, and 137 of tho
> 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
> Exercise 64 looked at distances PGA golfers can hit the ball. The standard deviation of these average drive distances is 11.2 yards, and the quartiles are Q1=282.05 yards and Q3=294.5 yards. 1. Write a sentence or two describing the spread in distances b
> 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
> We saw in Chapter 16, Exercise 36 that 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% r
> We learned in Chapter 16, Exercise 35 that 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 wor
> 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 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.
> 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 80
> 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
> Exercise 63 looked at the running times of movies released in 2010. The standard deviation of these running times is 16.6 minutes, and the quartiles are Q1=282.05 minutes and Q3=116 minutes. 1. Write a sentence or two describing the spread in running tim
> 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. 1. If there really were 6 vanilla an
> 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 tails. You try again and lose again. 1. Do two losses in a row convince you that he rea
> A survey investigating whether the proportion of today 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 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? E
> 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. 1. There a 3% chanc
> After the political ad campaign described in Exercise 15, part a, pollsters check the governor 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. Wh
> Write the null and alternative hypotheses you would use to test each situation. 1. In the 1950s, only about 40% of high school graduates went on to college. Has the percentage changed? 2. Twenty percent of cars of a certain model have needed costly trans
> Write the null and alternative hypotheses you would use to test each of the following situations: 1. A governor is concerned about his negatives the percentage of state residents who express disapproval of his job performance. His political committee pay
> 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 above 8 miles per hour, according to the Wind Ene
> The display shows the average drive distance (in yards) for 199 professional golfers during a week on the men PGA tour in 2015. 1. Describe this distribution. 2. Approximately what proportion of professional male golfers drive, on average, 280 yards or l
> The Professional Golfers Association reported the average distance that 199 professional golfers drove the ball (in yd) during a week in 2015. Here is a histogram of those drives. Assume this is a representative sample of all professional golfers. 1. Fin
> A tire manufacturer is considering a newly designed tread pattern for its all-weather tires. Tests have indicated that these tires will provide better gas mileage and longer tread life. The last remaining test is for braking effectiveness. The company ho
> Psychology experiments sometimes involve testing the ability of rats to navigate mazes. The mazes are classified according to difficulty, as measured by the mean length of time it takes rats to find the food at the end. One researcher needs a maze that w
> Reports tested 11 brands of vanilla yogurt and found these numbers of calories per serving: 1. Check the assumptions and conditions. 2. Create a 95% confidence interval for the average calorie content of vanilla yogurt. 3. A diet guide claims that you wi
> In 1998, as an 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 stati
> 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 un-popped, on average. Af
> 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. 1. a) Do these data satisfy the assumptions f
> Students investigating the packaging of potato chips purchased 6 bags of Lay Ruffles 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, 28.5.
> 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. 1. Explain why you suspect this distribution may be skewed to the right. 2. Explain why you could estimate the pro
> The histogram shows the running times in minutes of the 150 top-grossing feature films released in 2010. 1. You plan to see a movie this weekend. Based on these movies, how long do you expect a typical movie to run? 2. Would you be surprised to find that
> The duration of human pregnancies may not actually follow the Normal model described in Exercise 51 . 1. Explain why it may be somewhat skewed to the left. 2. If the correct model is in fact skewed, does that change your answers to parts a, b, and c of E
> Statistics from Cornell Northeast Regional Climate Center indicate that Ithaca, New York, gets an average of 35.4" of rain each year, with a standard deviation of 4.2". Assume that a Normal model applies. 1. During what percentage of years does Ithaca ge
> Assume that the duration of human pregnancies can be described by a Normal model with mean 266 days and standard deviation 16 days. 1. What percentage of pregnancies should last between 270 and 280 days? 2. At least how many days should the longest 25% o
> Allstate Insurance Company identified the 10 safest and 10 least-safe U.S. cities from among the 200 largest cities in the United States, based on the mean number of years drivers went between automobile accidents. The cities on both lists were all small
> A reporter working on a story about the New York lottery contacted one of the authors of this text, wanting help analyzing data to see if some ticket sales outlets were more likely to produce winners. His data for each of the 966 New York lottery outlets
> Assessment records indicate that the value of homes in a small city is skewed right, with a mean of $140,000 and standard deviation of $60,000. To check the accuracy of the assessment data, officials plan to conduct a detailed appraisal of 100 homes sele
> A college data about the incoming freshmen indicate that the mean of their high school GPAs was 3.4, with a standard deviation of 0.35; the distribution was roughly mound-shaped and only slightly skewed. The students are randomly assigned to freshman wri
> In Exercise 44 , you looked at the annual compensation for 800 CEOs, for which the true mean and standard deviation were (in thousands of dollars) 10,307.31 and 17,964.62, respectively. A simulation drew samples of sizes 30, 50, 100, and 200 (with replac
> Researchers measured the Waist Sizes of 250 men in a study on body fat. The true mean and standard deviation of the Waist Sizes for the 250 men are 36.33 inches and 4.019 inches, respectively. In Exercise 43 , you looked at the histograms of simulations
> The total compensation of the chief executive officers (CEOs) of the 800 largest U.S. companies (the Fortune 800) averaged (in thousands of dollars) 10,307.31 with a standard deviation (also in $1000) of 17,964.62. Here is a histogram of their annual com
> Look again at the histogram of men neck sizes in Exercise 60. 1. Is the mean closer to 14, 15, or 16 inches? Why? 2. Is the standard deviation closer to 1 inch, 3 inches, or 5 inches? Explain
> A study measured the Waist Size of 250 men, finding a mean of 36.33 inches and a standard deviation of 4.02 inches. Here is a histogram of these measurements: (Data in Body fat) 1. Describe the histogram of Waist Size. 2. To explore how the mean might va
> 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
> In Chapter 6, Exercise 41 , we examined the average fuel economy of 35 2016 model vehicles. (Data in Fuel economy 2016 with sample = Yes) 1. Find and interpret a 95% confidence interval for the gas mileage of 2016 vehicles. 2. Do you think that this conf
> The United States Golf Association (USGA) sets performance standards for golf balls. For example, the mean initial velocity of the ball may not exceed 250 feet per second when measured by an apparatus approved by the USGA. Suppose a manufacturer introduc
> A researcher investigates whether the mean cholesterol level among those who eat frozen pizza exceeds 220 mg/dL, the value considered to indicate a health risk. The confidence interval for the mean is (225.5, 240.8) mg/dL. Explain what this indicates for
> 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. A 90% confidence interval estimated the mean sodium content for this kind of hot dog at 317.2 to 326
> This chapter Examples 17.1 and 17.2 looked at mirex contamination in farmed salmon. We first found a 95% confidence interval for the mean concentration to be 0.0834 to 0.0992 parts per million (ppm). The EPA sets a limit of 0.08 ppm to be considered safe
> Will your flight get you to your destination on time? The Bureau of Transportation Statistics reported the percentage of flights that were delayed each month from 1994 through June of 2016. Here a histogram, along with some summary statistics: We can con
> What are the chances your flight will leave on time? The Bureau of Transportation Statistics of the U.S. Department of Transportation publishes information about airline performance. We saw the data in a Just Checking exercise in Chapter 4. Here are a hi
> After his first attempt to determine the speed of light (described in Exercise 33 ), Michelson conducted an improved experiment. In 1897, he reported results of 100 trials with a mean of 852.4 and a standard deviation of 79.0. 1. What is the standard err
> Look again at the histogram of the pizza prices in Exercise 59. 1. Is the mean closer to $2.40, $2.60, or $2.80? Why? 2. Is the standard deviation closer to $0.15, $0.50, or $1.00? Explain
> In 1882, Michelson measured the speed of light (usually denoted c as in Einstein famous equation E=mc2). His values are in km/sec and have 299,000 subtracted from them. He reported the results of 23 trials with a mean of 756.22 and a standard deviation o
> Suppose that, for budget planning purposes, the city in Exercise 30 needs a better estimate of the mean daily income from parking fees. 1. Someone suggests that the city use its data to create a 95% confidence interval instead of the 90% interval first c
> Consider again the statistics about human body temperature in Exercise 29 . 1. Would a 90% confidence interval be wider or narrower than the 98% confidence interval you calculated before? Explain. (Don’t compute the new interval.) 2. What are the advanta
> Hoping to lure more shoppers downtown, a city builds a new public parking garage in the central business district. The city plans to pay for the structure through parking fees. During a two-month period (44 weekdays), daily fees collected averaged $126,
> The researcher described in Exercise 23 also measured the body temperatures of that randomly selected group of adults. Here are summaries of the data he collected. We wish to estimate the average (or normal) temperature among the adult population. 1. Che
> In the latest National Health and Nutrition Examination Survey (NHANES 2013/2014 wwwn.cdc.gov/nchs/nhanes), pulse rate (30 sec rate multiplied by 2) of 2536 U.S. adults averaged 71.6 beats/min with a standard deviation of 11.5 beats/min. (Data in NHANES)
> In the latest National Health and Nutrition Examination Survey (NHANES 2013/2014 wwwn.cdc.gov/nchs/nhanes), HDL cholesterol of 2515 U.S. adults averaged 53.9 mg/dL with a standard deviation of 16.2729 mg/dL. (Data in NHANES) 1. Can you apply the Central
> A credit card company takes a random sample of 100 cardholders to see how much they charged on their card last month. Here a histogram. A computer program found that the resulting 95% confidence interval for the mean amount spent in March 2011 is ($28,36
