Question: You are among 100 people attending a

> Using a computer to play many simulated games of Scrabble, researcher Charles Robinove found that the letter A occurred in 54% of the hands. This study had a margin of error of ±10% (Chance, 15, no. 1 [2002]) 1. Explain what the margin of error means in

> In a survey of 1002 U.S. adults in December 2016 by Pew Research (www.journalism.org/2016/12/15/many-americans-believe-fake-news-is-sowing-confusion/), 64% of adult respondents say they think that made-up news is causing a great deal of confusion about t

> A high school senior uses the Internet to get information on February temperatures in the town where he’ll be going to college. He finds a website with some statistics, but they are given in degrees Celsius. The conversion formula is F=9/5 C+32. Determin

> The fastest horse in Kentucky Derby history was Secretariat in 1973. The scatterplot shows speed (in miles per hour) of the winning horses each year. What do you see? In most sporting events, performances have improved and continue to improve, so surely

> The 2016 U.S. presidential election was unusual in several ways. First, the candidate who won the most electoral votes, Donald Trump, did not win the most popular votes. Second, several minor-party candidates received enough votes to possibly affect the

> In a car rental company fleet, 70% of the cars are American brands, 20% are Japanese, and the rest are German. The company notes that manufacturers recalls seem to affect 2% of the American cars, but only 1% of the others. 1. What the probability that a

> How large are hamster litters? Among 47 golden hamster litters recorded, there were an average of 7.72 baby hamsters, with a standard deviation of 2.5 hamsters per litter. 1. Create and interpret a 90% confidence interval. 2. Would a 98% confidence inter

> We work for the Watchdog for the Consumer consumer advocacy group. We’ve been asked to look at a battery company that claims its batteries last an average of 100 hours under normal use. There have been several complaints that the batteries don’t last tha

> Every statement about a confidence interval contains two parts the level of confidence and the interval. Suppose that an insurance agent estimating the mean loss claimed by clients after home burglaries created the 95% confidence interval ($1644, $2391).

> As a project for an Introductory Statistics course, students checked 6 bags of Fritos marked with a net weight of 35.4 grams. They carefully weighed the contents of each bag, recording the following weights (in grams): 35.5, 35.3, 35.1, 36.4, 35.4, 35.5.

> Clarksburg Bakery is trying to predict how many loaves to bake. In the past 100 days, the bakery has sold between 95 and 140 loaves per day. Here are a histogram and the summary statistics for the number of loaves sold for the past 100 days. 1. Can you u

> In February 2012, MedPage Today reported that researchers used vemurafenib to treat metastatic melanoma (skin cancer). Out of 152 patients, 53% had a partial or complete response to vemurafenib. 1. Write a 95% confidence interval for the proportion helpe

> Researchers in the Adirondack Mountains collect data on a random sample of streams each year. One of the variables recorded is the substrate of the stream the type of soil and rock over which they flow. The researchers found that 69 of the 172 sampled st

> In 2011, the Occupy Wall Street movement protested the concentration of wealth and power in the United States. A 2012 University of Delaware survey asked a random sample of 901 American adults whether they agreed or disagreed with the following statement

> Each year thousands of high school students take either the SAT or the ACT, standardized tests used in the college admissions process. Combined SAT Math and Verbal scores go as high as 1600, while the maximum ACT composite score is 36. Since the two exam

> A college student is on a meal program. His budget allows him to spend an average of $10 per day for the semester. He keeps track of his daily food expenses for 2 weeks; the data are given in the table below. Is there strong evidence that he will overspe

> To get a voter initiative on a state ballot, petitions that contain at least 250,000 valid voter signatures must be filed with the Elections Commission. The board then has 60 days to certify the petitions. A group wanting to create a statewide system of

> A newspaper report in August 2002 raised the issue of racial bias in the issuance of speeding tickets. The following facts were noted: Sixteen percent of drivers registered in New Jersey are black. Of the 324 speeding tickets issued in one month on a 65-

> Medical literature says that about 8% of males are color-blind. A university introductory psychology course is taught in a large lecture hall. Among the students, there are 325 males. Each semester when the professor discusses visual perception, he shows

> The U.S. Census Bureau reports that 36% of all U.S. businesses are owned by women (www.entrepreneur.com/article/252048). A Colorado consulting firm surveys a random sample of 410 businesses in the Denver area and finds that 164 of them have women owners.

> One study comparing various treatments for the eating disorder anorexia nervosa initially enlisted 198 subjects, but found overall that 105 failed to complete their assigned treatment programs. Construct and interpret an appropriate confidence interval.

> The advertising company described in Exercise R5.26 is thinking about signing a WNBA star to an endorsement deal. In its poll, 27% of the respondents could identify her. 1. Fans who never took statistics can’t understand why the company did not offer thi

> An advertising agency won’t sign an athlete to do product endorsements unless it is sure the person is known to more than 25% of its target audience. The agency always conducts a poll of 500 people to investigate the athlete name recognition before offer

> In 1996, 20% of all students at a major university had an overall grade point average of 3.5 or higher (on a scale of 4.0). In 2012, a random sample of 1100 student records found that 25% had a GPA of 3.5 or higher. Is this evidence of grade inflation?

> President Obama was very popular at the end of his eight years in office. A CNN/ORC poll of 1000 U.S. adults conducted in the week before the end of his term found that 63% of Americans said they held a favorable view of the President (elections.huffingt

> A specialty foods company sells gourmet hams by mail order. The hams vary in size from 4.15 to 7.45 pounds, with a mean weight of 6 pounds and standard deviation of 0.65 pounds. The quartiles and median weights are 5.6, 6.2, and 6.55 pounds. 1. Find the

> We are replicating an experiment. How will each of the following changes affect the power of our test? Indicate whether it will increase, decrease, or remain the same, assuming that all other aspects of the situation remain unchanged. 1. We increase the

> A computer company recently experienced a disastrous fire that ruined some of its inventory. Unfortunately, during the panic of the fire, some of the damaged computers were sent to another warehouse, where they were mixed with undamaged computers. The en

> Observers in Texas watched children at play in eight communities. Of the 814 children seen biking, roller skating, or skateboarding, only 14% wore a helmet. 1. Create and interpret an appropriate 95% confidence interval. 2. What concerns do you have abou

> An auto parts company advertises that its special oil additive will make the engine run smoother, cleaner, longer, with fewer repairs. An independent laboratory decides to test part of this claim. It arranges to have a taxicab company fleet of cars use t

> A champion archer can generally hit the bull-eye 80% of the time. Suppose she shoots 200 arrows during competition. Let p^ represent the percentage of bull-eyes she gets (the sample proportion). 1. What are the mean and standard deviation of the sampling

> Growing concern about binge drinking among college students has prompted one large state university to conduct a survey to assess the size of the problem on its campus. The university plans to randomly select students and ask how many have been drunk dur

> The Centers for Disease Control and Prevention reports that 9.3% of surveyed high school students reported in 2015 that they had smoked cigarettes in the past 30 days. A college has 522 students in its freshman class. How likely is it that more than 10%

> The 2014 U.S. Religious Landscape Study interviewed more than 35,000 Americans from all 50 states about their beliefs and the role of religion in their lives. The fastest-growing group is the 22.8% who are Nones those who are not affiliated with any orga

> Neurological research has shown that in about 80% of people language abilities reside in the brain left side. Another 10% display right-brain language centers, and the remaining 10% have two-sided language control. (The latter two groups are mainly left-

> A Rutgers University study found that many high school students cheat on tests. The researchers surveyed a random sample of 4500 high school students nationwide; 74% of them said they had cheated at least once. 1. Create a 90% confidence interval for the

> Here are the summary statistics for the weekly payroll of a small company: lowest salary=$300, mean salary=$700, median=$500, range=$1200, IQR=$600, first quartile=$350, standard deviation=$400. 1. Do you think the distribution of salaries is symmetric,

> Organizers of a fishing tournament believe that the lake holds a sizable population of largemouth bass. They assume that the weights of these fish have a model that is skewed to the right with a mean of 3.5 pounds and a standard deviation of 2.2 pounds.

> One of the important issues for poultry farmers is the production rate the percentage of days on which a given hen actually lays an egg. Ideally, that would be 100% (an egg every day), but realistically, hens tend to lay eggs on about 3 of every 4 days.

> A newspaper article that reported the results of an election poll included the following explanation: The Associated Press poll on the 2016 presidential campaign is based on telephone interviews with 798 randomly selected registered voters from all state

> According to the U.S. American Community Survey (ACS), by 2014, for the first time in the history of the ACS, more U.S. 18- to 34-year-olds reported living with a parent than were living independently in their own homes. The survey found that 32.1% were

> The 2016 State of Women-Owned Businesses Report commissioned by American Express (www.womenable.com/70/the-state-of-women-owned-businesses-in-the-u.s.:-2016) says that, excluding large, publicly traded firms, women-owned firms make up 38% of the privatel

> The National Perinatal Statistics Unit of the Sydney Children Hospital reports that the mean birth weight of all babies born in birth centers in Australia in a recent year was 3564 grams about 7.86 pounds. A Missouri hospital reports that the average wei

> A group of 5 women became pregnant while undergoing fertility treatments with the drug Clomid, discussed in Exercise 7 . What the probability that 1. none will have twins? 2. exactly 1 will have twins? 3. at least 3 will have twins?

> A car owner may buy insurance that will pay the full price of repairing the car after an at-fault accident, or save $12 a year by getting a policy with a $500 deductible. Her insurance company says that about 0.5% of drivers in her area have an at-fault

> In the United States, the probability of having twins (usually about 1 in 90 births) rises to about 1 in 10 for women who have been taking the fertility drug Clomid. Among a group of 10 pregnant women, what the probability that 1. at least one will have

> Safety engineers must determine whether industrial workers can operate a machine emergency shutoff device. Among a group of test subjects, 66% were successful with their left hands, 82% with their right hands, and 51% with both hands. 1. What percent of

> The mean price of pizza in Baltimore was $2.85, $0.23 higher than the mean price of $2.62 in Dallas. To see if that difference was real, or due to chance, we took the 156 prices from Baltimore and Dallas and mixed those 312 prices together. Then we rando

> To play a game, you must pay $5 for each play. There is a 10% chance you will win $5, a 40% chance you will win $7, and a 50% chance you will win only $3. 1. What are the mean and standard deviation of your net winnings? 2. You play twice. Assuming the p

> Suppose that 70% of the women who suspect they may be pregnant and purchase an in-home pregnancy test are actually pregnant. Further suppose that the test is 98% accurate. What the probability that a woman whose test indicates that she is pregnant actual

> In a car rental company fleet, 70% of the cars are American brands, 20% are Japanese, and the rest are German. The company notes that manufacturers recalls seem to affect 2% of the American cars, but only 1% of the others. 1. What the probability that a

> In 1961 astronomer Frank Drake developed an equation to try to estimate the number of extraterrestrial civilizations in our galaxy that might be able to communicate with us via radio transmissions. Now largely accepted by the scientific community, the Dr

> A coin is to be tossed 36 times. 1. What are the mean and standard deviation of the number of heads? 2. Suppose the resulting number of heads is unusual, two standard deviations above the mean. How many extra heads were observed? 3. If the coin were toss

> Psychiatrists estimate that about 1 in 100 adults suffers from bipolar disorder. What the probability that in a city of 10,000 there are more than 200 people with this condition? Be sure to verify that a Normal model can be used here.

> In your sock drawer you have 4 blue socks, 5 gray socks, and 3 black ones. Half asleep one morning, you grab 2 socks at random and put them on. Find the probability you end up wearing 1. 2 blue socks. 2. no gray socks. 3. at least 1 black sock. 4. a gree

> Almost every year, there is some incidence of volcanic activity on the island of Japan. In 2005 there were 5 volcanic episodes, defined as either eruptions or sizable seismic activity. Suppose the mean number of episodes is 2.4 per year. Let X be the num

> Failures of O-rings on the space shuttle are fairly rare, but often disastrous, events. If we are testing O-rings, suppose that the probability of a failure of any one O-ring is 0.01. Let X be the number of failures in the next 10 O-rings tested. 1. What

> The company that sells frozen pizza to stores in four markets in the United States (Denver, Baltimore, Dallas, and Chicago) wants to examine the prices that the stores charge for pizza slices. Here are boxplots comparing data from a sample of stores in e

> A census by the county dog control officer found that 18% of homes kept one dog as a pet, 4% had two dogs, and 1% had three or more. If a salesman visits two homes selected at random, what the probability he encounters 1. no dogs? 2. some dogs? 3. dogs i

> Every 5 years the Conference Board of the Mathematical Sciences surveys college math departments. In 2000 the board reported that 51% of all undergraduates taking Calculus I were in classes that used graphing calculators and 31% were in classes that used

> Here another attempt at developing a good strategy for the dice game in Exercise 33 . Instead of stopping after a certain number of rolls, you could decide to stop when your score reaches a certain number of points. 1. How many points would you expect a

> When to stop In Exercise 27 of the Review Exercises for Part III, we posed this question: You play a game that involves rolling a die. You can roll as many times as you want, and your score is the total for all the rolls. But if you roll a 6, your score

> A Statistics professor comes home to find that all four of his children got white team shirts from soccer camp this year. He concludes that this year, unlike other years, the camp must not be using a variety of colors. But then he finds out that in each

> The 2013 State of Women-Owned Businesses Report commissioned by American Express (www.womenable.com/content/userfiles/2013_State_of_WomenOwned_Businesses_Report_FINAL.pdf) says that, excluding large, publicly traded firms, women-owned firms make up 30% o

> The first store in Exercise 28 sells watermelons for 32 cents a pound. The second store is having a sale on watermelons only 25 cents a pound. Find the mean and standard deviation of the difference in the price you may pay for melons randomly selected at

> Each year a company must send 3 officials to a meeting in China and 5 officials to a meeting in France. Airline ticket prices vary from time to time, but the company purchases all tickets for a country at the same price. Past experience has shown that ti

> According to the 2000 Census, 66% of U.S. households own the home they live in. A mayoral candidate conducts a survey of 820 randomly selected homes in your city and finds only 523 owned by the current residents. The candidate then attacks the incumbent

> Two stores sell watermelons. At the first store the melons weigh an average of 22 pounds, with a standard deviation of 2.5 pounds. At the second store the melons are smaller, with a mean of 18 pounds and a standard deviation of 2 pounds. You select a mel

> From Exercise 50 it appeared that the mean log fusion time for the VV group was greater than that of the NV group. Could the difference be due to chance? The histogram below shows the difference in the means of the log fusion times by randomly selecting

> Your pocket copy of Kyrgyzstan on 4237±360 Som a Day claims that you can expect to spend about 4237 som each day with a standard deviation of 360 som. How well can you estimate your expenses for the trip? 1. Your budget allows you to spend 90,000 som. To

> A college student on a seven-day meal plan reports that the amount of money he spends daily on food varies with a mean of $13.50 and a standard deviation of $7. 1. What are the mean and standard deviation of the amount he might spend in two consecutive d

> According to a recent Gallup survey, 93% of teens use the Internet, but there are differences in how teen boys and girls say they use computers. The telephone poll found that 77% of boys had played computer games in the past week, compared with 65% of gi

> Explain why the facts you know about variances of independent random variables might encourage two small insurance companies to merge. (Hint: Think about the expected amount and potential variability in payouts for the separate and the merged companies.)

> Given independent random variables with means and standard deviations as shown, find the mean and standard deviation of each of these variables: 1. X+50 2. 10Y 3. X+0.5Y 4. XY 5. X+Y

> Suppose that, as reported by the Centers for Disease Control, about 18% of high school students smoke tobacco. You randomly select 120 high school students to survey them on their attitudes toward scenes of smoking in the movies. 1. What the expected num

> Molly college offers two sections of Statistics 101. From what she has heard about the two professors listed, Molly estimates that her chances of passing the course are 0.80 if she gets Professor Scedastic and 0.60 if she gets Professor Kurtosis. The reg

> The Centers for Disease Control and Prevention say that about 18% of high-school students smoke tobacco (down from a high of 38% in 1997). Suppose you randomly select high-school students to survey them on their attitudes toward scenes of smoking in the

> A company human resources officer reports a breakdown of employees by job type and sex shown in the table. 1. What the probability that a worker selected at random is 1. female? 2. female or a production worker? 3. female, if the person works in producti

> A 65-year-old woman takes out a $100,000 term life insurance policy. The company charges an annual premium of $520. Estimate the company expected profit on such policies if mortality tables indicate that only 2.6% of women age 65 die within a year.

> From Exercise 16 it appeared that the mean cost of a cappuccino was slightly higher than the mean cost of a dozen eggs. Given the variation among the prices, could that difference be due just to chance? To examine that further, we took 1000 random sample

> Many investment advisors argue that after stocks have declined in value for 2 consecutive years, people should invest heavily because the market rarely declines 3 years in a row. 1. Since the stock market began in 1872, there have been two consecutive lo

> A multiple choice test has 50 questions, with 4 answer choices each. You must get at least 30 correct to pass the test, and the questions are very difficult. 1. Are you likely to be able to pass by guessing on every question? Explain. 2. Suppose, after s

> Since the stock market began in 1872, stock prices have risen in about 73% of the years. Assuming that market performance is independent from year to year, what the probability that 1. the market will rise for 3 consecutive years? 2. the market will rise

> In some cities tall people who want to meet and socialize with other tall people can join Beanstalk Clubs. To qualify, a man must be over 6²2³ tall, and a woman over 5²10³. According to the National Health Survey, heights of adults may have a Normal mode

> If you land in a penalty zone on the game board described in Exercise 12 , your move will be determined by subtracting the roll of the die from the result on the spinner. Now what are the mean and standard deviation of the number of spots you may move?

> Neurological research has shown that in about 80% of people, language abilities reside in the brain left side. Another 10% display right-brain language centers, and the remaining 10% have two-sided language control. (The latter two groups are mainly left

> In a board game you determine the number of spaces you may move by spinning a spinner and rolling a die. The spinner has three regions: Half of the spinner is marked 5, and the other half is equally divided between 10 and 20. The six faces of the die sho

> At a large fertility clinic, 152 women became pregnant while taking Clomid. (See Exercise 7 .) 1. What are the mean and standard deviation of the number of twin births we might expect? 2. Can we use a Normal model in this situation? Explain. 3. What the

> The car insurance company in Exercise 8 believes that about 0.5% of drivers have an at-fault accident during a given year. Suppose the company insures 1355 drivers in that city. 1. What are the mean and standard deviation of the number who may have at-fa

> A consumer organization estimates that 29% of new cars have a cosmetic defect, such as a scratch or a dent, when they are delivered to car dealers. This same organization believes that 7% have a functional defect something that does not work properly and

> Because of the skewness of the distributions of fusion times described in Exercise 49, we might consider a re-expression. Here are the boxplots of the log of fusion times. Is it better to analyze the original fusion times or the log fusion times? Explain

> Does keeping a child lunch in an insulated bag, even with ice packs, protect the food from warming to temperatures where germs can proliferate? Researchers used an electric temperature gun on 235 lunches at preschools 90 minutes before they were to be ea

> People who read the last page of a mystery novel first generally like stories better. Researchers recruited 819 college students to read short stories, and for one story, they were given a spoiler paragraph beforehand. On the second and third story, the

> Fireworks manufacturers face a dilemma. They must be sure that the rockets work properly, but test-firing a rocket essentially destroys it. On the other hand, not testing the product leaves open the danger that they sell a bunch of duds, leading to unhap

> In the journal Science, a research team reported that plants in southern England are flowering earlier in the spring. Records of the first flowering dates for 385 species over a period of 47 years indicate that flowering has advanced an average of 15 day

> Data were collected over a decade from 1021 men and women with a recent history of precancerous colon polyps. Participants were randomly assigned to receive folic acid (a B vitamin) or a placebo, and the study concluded that those receiving the folic aci

> Carsten, Matt, and Rainer designed an experiment to see how different environments affect the Internet speed around campus. They used their own Mac computer and a PC belonging to the school and tested each in two different libraries, the main and the sci

> There are 20 first-class passengers and 120 coach passengers scheduled on a flight. In addition to the usual security screening, 10% of the passengers will be subjected to a more complete search. 1. Describe a sampling strategy to randomly select those t

> Wayne Collier designed an experiment to measure the fuel efficiency of his family car under different tire pressures. For each run, he set the tire pressure to either 28 or 32 psi and then measured the miles driven on a highway (I-95 between Mills River

> The radioactive gas radon, found in some homes, poses a health risk to residents. To assess the level of contamination in their area, a county health department wants to test a few homes. If the risk seems high, they will publicize the results to emphasi