Question: In 1882, Michelson measured the speed of

> 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

> 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. 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

> 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

> A sample of 20 CEOs from the Forbes 500 shows total annual compensations ranging from a minimum of $0.1 to $62.24 million. The average for these 20 CEOs is $7.946 million. Here a histogram: Based on these data, a computer program found that a 95% confide

> Data collected by child development scientists produced this confidence interval for the average age (in weeks) at which babies begin to crawl: t-Interval for μ(95.00% Confidence)30.65

> The histogram shows the neck sizes (in inches) of the 250 men recruited for the health study in Utah from Exercise 9. (Data in Bodyfat. The neck sizes in Bodyfat are in cm. Divide by 2.54 for inches.) Which summary statistics would you choose to summariz

> Cornell University has used a lake source cooling plant that circulates water from Cayuga Lake through a heat transfer system to chill water for use on campus in refrigeration and air conditioning. Supporters of this method cite reduced carbon emissions

> A medical researcher measured the pulse rates (beats per minute) of a sample of randomly selected adults and found the following Student t-based confidence interval: With 95.00% Confidence,70.887604

> A TV news reporter says that a proposed constitutional amendment is likely to win approval in the upcoming election because a poll of 1505 likely voters indicated that 52% would vote in favor. The reporter goes on to say that the margin of error for this

> A newspaper reports that the governor 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?

> Suppose ACT, Inc. wants to update their information from Exercise 46 on the percentage of freshmen that return for a second year of college. 1. They want to cut the stated margin of error in half. How many college freshmen must be surveyed? 2. Do you hav

> Wildlife biologists inspect 153 deer taken by hunters and find 32 of them carrying ticks that test positive for Lyme disease. 1. Create a 90% confidence interval for the percentage of deer that may carry such ticks. 2. If the scientists want to cut the m

> Inc. reported that 74% of 1644 randomly selected college freshmen returned to college the next year. The study was stratified by type of college public or private. The retention rates were 71.9% among 505 students enrolled in public colleges and 74.9% am

> In January 2014 AP-GfK polled 1060 U.S. adults to find if people were more concerned with privacy or security. Privacy concerns outweighed concerns about being safe from terrorists for 646 out of the 1060 polled. Of the 1060 adults, about 180 are 65 and

> A 2011 Gallup Poll found that 76% of Americans believe that high achieving high school students should be recruited to become teachers. This poll was based on a random sample of 1002 Americans. 1. Find a 90% confidence interval for the proportion of Amer

> Vitamin D, whether ingested as a dietary supplement or produced naturally when sunlight falls on the skin, is essential for strong, healthy bones. The bone disease rickets was largely eliminated in England during the 1950s, but now there is concern that

> A city ballot includes a local initiative that would legalize gambling. The issue is hotly contested, and two groups decide to conduct polls to predict the outcome. The local newspaper finds that 53% of 1200 randomly selected voters plan to vote yes, whi

> The histogram shows the distribution of the prices of plain pizza slices (in $) for 156 weeks in Dallas, TX. Which summary statistics would you choose to summarize the center and spread in these data? Why?

> In the survey on the death penalty you read about in the Step-by-Step Example, the Gallup Poll actually split the sample at random, asking 510 respondents the question quoted earlier, Generally speaking, do you believe the death penalty is applied fairly

> 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 survey

> Junk mail Direct mail advertisers send solicitations (a.k.a. junk mail) to thousands of potential customers in the hope that some will buy the company product. The acceptance rate is usually quite low. Suppose a company wants to test the response to a ne

> An insurance company checks police records on 582 accidents selected at random and notes that teenagers were at the wheel in 91 of them. 1. Create a 95% confidence interval for the percentage of all auto accidents that involve teenage drivers. 2. Explain

> First USA, a major credit card company, is planning a new offer for their current cardholders. The offer will give double airline miles on purchases for the next 6 months if the cardholder goes online and registers for the offer. To test the effectivenes

> The Paralyzed Veterans of America is a philanthropic organization that relies on contributions. They send free mailing labels and greeting cards to potential donors on their list and ask for a voluntary contribution. To test a new campaign, they recently

> The Pew Research poll described in Exercise 5 found that 56% of a sample of 1060 teens go online several times a day. (Treat this as a Simple Random Sample.) 1. Find the margin of error for this poll if we want 95% confidence in our estimate of the perce

> In a poll taken in December 2012, Gallup asked 1006 national adults whether they were baseball fans; 48% said they were. Almost five years earlier, in February 2008, only 35% of a similar-size sample had reported being baseball fans. 1. Find the margin o

> A Consumer Reports study similar to the one described in Exercise 31 found that 12 of the 22 red snapper packages tested were a different kind of fish. 1. Are the conditions for creating a confidence interval satisfied? Explain. 2. Construct a 95% confid

> Using the data from Exercise 56, write up a short report describing the distribution of the number of deaths in the United States from tornadoes during this time period

> In 2013 the environmental group Oceana (usa.oceana.org) analyzed 1215 samples of seafood purchased across the United States and genetically compared the pieces to standard gene fragments that can identify the species. Laboratory results indicated that 33

> A study of 902 decisions (to grant parole or not) made by the Nebraska Board of Parole produced the following computer output. Assuming these cases are representative of all cases that may come before the Board, what can you conclude? z-Interval for prop

> What fraction of cars made in Japan? The computer output below summarizes the results of a random sample of 50 autos. Explain carefully what it tells you. z-Interval for proportion With 90.00% confidence,0.29938661

> Several factors are involved in the creation of a confidence interval. Among them are the sample size, the level of confidence, and the margin of error. Which statements are true? 1. For a given sample size, reducing the margin of error will mean lower c

> Several factors are involved in the creation of a confidence interval. Among them are the sample size, the level of confidence, and the margin of error. Which statements are true? 1. For a given sample size, higher confidence means a smaller margin of er

> In January 2002, two students made worldwide headlines by spinning a Belgian euro 250 times and getting 140 heads that 56%. That makes the 90% confidence interval (51%, 61%). What does this mean? Are these conclusions correct? Explain. 1. Between 51% and

> A catalog sales company promises to deliver orders placed on the Internet within 3 days. Follow-up calls to a few randomly selected customers show that a 95% confidence interval for the proportion of all orders that arrive on time is 88%±6%. What does t

> Consider each situation described. Identify the population and the sample, explain what p and p^ represent, and tell whether the methods of this chapter can be used to create a confidence interval. 1. A consumer group hoping to assess customer experience

> For each situation described below, identify the population and the sample, explain what p and p^ represent, and tell whether the methods of this chapter can be used to create a confidence interval. 1. Police set up an auto checkpoint at which drivers ar

> A medical researcher estimates the percentage of children exposed to lead-based paint, adding that he believes his estimate has a margin of error of about 3%. Explain what the margin of error means.

> Using the data from Exercise 55, write a short report describing the distribution of the number of deaths in the United States from floods during this time period.

> A TV newscaster reports the results of a poll of voters, and then says, The margin of error is plus or minus 4%. Explain carefully what that means.

> In an effort to improve the quality of their cell phones, a manufacturing manager records the number of faulty phones in each day production run. The manager notices that the number of faulty cell phones in a production run of cell phones is usually smal

> A website manager has noticed that during the evening hours, about 3 people per minute check out from their shopping cart and make an online purchase. She believes that each purchase is independent of the others and wants to model the number of purchases

> The archer in Exercise 56 continues shooting arrows, ending up with 45 bull-eyes in 50 shots. Now are you convinced that the new bow is better? Explain.

> The basketball player in Exercise 55 has new sneakers, which he thinks improve his game. Over his past 40 shots, he made 32 much better than the 55% he usually shoots. Do you think his chances of making a shot really increased? In other words, is making

> The archer in Exercise 30 purchases a new bow, hoping that it will improve her success rate to more than 80% bull-eyes. She is delighted when she first tests her new bow and hits 6 consecutive bull-eyes. Do you think this is compelling evidence that the

> A basketball player who ordinarily makes about 55% of his free throw shots has made 4 in a row. Is this evidence that he has a hot hand tonight? That is, is this streak so unusual that it means the probability he makes a shot must have changed? Explain.