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Statistics Concepts And Controversies 10th Edition David S. Moore, William I. Notz - Solutions

23.13 Searching for ESP. A researcher looking for evidence of extrasensory perception(ESP) tests 200 subjects. Only one of these subjects does significantly better (P
23.12 How far do rich parents take us? How much education children get is strongly associated with the wealth and social status of their parents. In social science jargon, this is socioeconomic status (SES). But the SES of parents has little influence on whether children who have graduated from
23.11 Legalizing marijuana. An October 2018 Gallup Poll found that 66% of the SRS of American adults surveyed support the legalization of marijuana in the United States. The poll had a margin of sampling error of ±4 percentage points at 95% confidence.a. Why do the results of this survey suggest
23.10 How do we feel? A Gallup Poll taken in late October 2011 found that 58% of the SRS of American adults surveyed, reflecting on the day before they were surveyed, said they experienced a lot of happiness and enjoyment without a lot of stress and worry. The poll had a margin of sampling error of
23.9 Soccer salaries. Paris Saint-Germain, a French professional soccer team, led the 2015 ESPN/Sporting Intelligence Global Salary Survey with the largest payroll for all professional sports teams. A soccer fan looks up the salaries for all of the players on the 2015 Paris Saint-Germain team.
23.8 A television poll. The Channel 13 news program conducts a call-in poll about the salaries of business executives. Of the 2372 callers, 1921 (or 81%) believe that business executives are vastly overpaid and that their pay should be substantially reduced. The station, following recommended
23.7 Sacred significance level. A researcher decided prior to conducting research to use a 1% level of significance. The researcher finds a P-value of 0.027. Is it okay for the researcher to change the significance level to 5% to have statistically significant results?a. No, because the
23.6 Practically significant? Brook conducted a study for a clothing company to determine if a rewards program caused customers to spend more. Brook found statistically significant results, with a P-value of 0.012. The average amount spent per order before the rewards program was $100, while the
23.5 Practically significant? A new blend of gasoline costs $1.00 more per gallon than regular gasoline. Tests have shown that gas mileage with the new blend is statistically significantly higher than that of regular gasoline. The P-value was 0.004. A report about these results goes on to say that
23.4 Width of a confidence interval. Suppose that the length of a confidence interval is 0.06 when the sample size is 400. To decrease the length of the confidence interval to 0.03, we should take a sample of sizea. 100.b. 200.c. 800.d. 1600.
23.3 Finding statistical significance. If we conduct 100 hypothesis tests at the 5% level, how many of them would we expect to be statistically significant just by chance alone?a. 0b. 5c. 95d. 100
4. What are some other things that would be helpful to know about the methods used in the original research study? Please explain.
3. Why would it be problematic to rely on retrospective reports of what the women ate prior to conceiving their babies?
2. In the original research study, the researchers mention that because of the multiplicity of testing, they only considered results to be significant if the P-value was less than 0.01.Why is this important?
1. Why is it not surprising that 1 food item out of 133 food items was found to be related to the sex of a baby?
22.40 Why should the significance level matter? On June 15, 2005, an article by Lawrence K. Altman appeared in the New York Times. The title of the article was “Studies Rebut Earlier Report on Pledges of Virginity.” The article mentioned that in two studies conducted by the Heritage Foundation,
22.39 Bad weather, bad tip? People tend to be more generous after receiving good news.Are they less generous after receiving bad news? The average tip left by adult Americans is 20%. Give 20 patrons of a restaurant a message on their bill warning them that tomorrow’s weather will be bad and
22.38 Will they charge more? A bank wonders whether omitting the annual credit card fee for customers who charge at least $3000 in a year will increase the amount charged on its credit cards. The bank makes this offer to an SRS of 400 of its credit card customers. It then compares how much these
22.37 Testing a random number generator. Our statistical software has a “random number generator” that is supposed to produce numbers scattered at random from 0 to 1. If this is true, the numbers generated come from a population with μ=0.5. A command to generate 100 random numbers gives
22.36 Response time. Last year, your company’s service technicians took an average of 2.5 hours to respond to trouble calls from business customers who had purchased service contracts. Do this year’s data show a significantly different average response time? What null and alternative hypotheses
22.35 Mice in a maze. Experiments on learning in animals sometimes measure how long it takes mice to find their way through a maze. The mean time is 19 seconds for one particular maze. A researcher thinks that a loud noise will cause the mice to complete the maze faster.She measures how long each
22.34 Student attitudes. The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures students’ study habits and attitudes toward school. Scores range from 0 to 200. The mean score for U.S. college students is about 115, and the standard deviation is about 30. A teacher
22.33 Speeding. It often appears that most drivers on the road are driving faster than the posted speed limit. Situations differ, of course, but here is one set of data. Researchers studied the behavior of drivers on a rural interstate highway in Maryland where the speed limit was 55 miles per
22.32 Do chemists have more girls? Some people think that chemists are more likely than other parents to have female children. (Perhaps chemists are exposed to something in their laboratories that affects the sex of their children.) The Washington State Department of Health lists the parents’
22.31 Side effects. An experiment on the side effects of pain relievers assigned arthritis patients to one of several over-the-counter pain medications. Of the 420 patients who took one brand of pain reliever, 21 suffered some “adverse symptom.”a. If 10% of all patients suffer adverse symptoms,
22.30 Interpreting scatterplots. In 2014, the Pew Research Centers American Trends Panel sought to better understand what Americans know about science. It was observed that among a random selection of 3278 adults, 2065 adults could correctly interpret a scatterplot. Is this good evidence that more
22.29 AP courses. Return to the study in Exercise 22.20, which found that 46 of 200 firstyear students said that they had not taken any AP courses in high school. Carry out the hypothesis test described in Exercise 22.20 and compute the P-value. How does your value compare with the value given in
22.28 Finding a P-value by simulation. A classic experiment to detect extra-sensory perception (ESP) uses a shuffled deck of cards containing five suits (waves, stars, circles, squares, and crosses). As the experimenter turns over each card and concentrates on it, the subject guesses the suit of
22.27 Finding a P-value by simulation. Is a new method of teaching reading to first-graders(Method B) more effective than the method now in use (Method A)? You design a matched pairs experiment to answer this question. You form 20 pairs of first-graders, with the two children in each pair carefully
22.26 Significance means what? Asked to explain the meaning of “statistically significant at the α=0.05 level,” a student says: “This means that the probability that the null hypothesis is true is less than 0.05.” Is this explanation correct? Why or why not?
22.25 Significant at what level? Explain in plain language why a result that is significant at the 1% level must always be significant at the 5% level. If a result is significant at the 5%level, what can you say about its significance at the 1% level?
22.24 Vote for the best face? Is the result of Exercise 22.21 statistically significant at the 5%level? At the 1% level?
22.23 AP courses. Is the result of Exercise 22.20 statistically significant at the 5% level? At the 1% level?
22.22 Do our athletes graduate? Is the result of Exercise 22.19 statistically significant at the 10% level? At the 5% level?
22.21 Vote for the best face? We often judge other people by their faces. It appears that some people judge candidates for elected office by their faces. Psychologists showed headand-shoulders photos of the two main candidates in 32 races for the U.S. Senate to many subjects (dropping subjects who
22.20 AP courses. In 2016, 17.6% of first-year college students responding to a national survey said that they had not taken any Advanced Placement (AP) courses in high school.Administrators at a large state university believe that more than 17.6% of their first-year students have not taken any AP
22.19 Do our athletes graduate? The National Collegiate Athletic Association (NCAA)requires colleges to report the graduation rates of their athletes. At one large university, 82%of all students who entered in 2012 graduated within six years. One hundred forty-nine of the 190 students who entered
22.18 Living on campus. A UCLA survey of college freshmen in the 2016–2017 academic year found that 74.8% of all first-year college students planned to live on campus. You wonder if this percentage is different at your school, but you have no idea whether it is higher or lower. You plan a sample
22.17 Unemployment. The national unemployment rate in a recent month was 5.1%. You think the rate may be different in your city, so you plan a sample survey that will ask the same questions as the Current Population Survey. To see if the local rate differs significantly from 5.1%, what hypotheses
22.16 Body temperature. We have all heard that 98.6 degrees Fahrenheit (or 37 degrees Celsius) is “normal body temperature.” In fact, there is evidence that most people have a slightly lower body temperature. You plan to measure the body temperature of a random sample of people very accurately.
22.15 Attending church. A recent survey by a national polling firm finds that 39% of American adults say they attended religious services last week. There is reason to suspect this percentage is not accurate.a. Why might we expect answers to a poll about attending religious services to overstate
22.14 What’s a gift worth? Do people value gifts from others more highly than they value the money it would take to buy the gift? We would like to think so because we hope that “the thought counts.” A survey of 209 adults asked them to list three recent gifts and then asked,“Aside from any
22.13 Ancient Egypt. Settlements in Egypt before the time of the pharaohs are dated by measuring the presence of forms of carbon that decay over time. The first datings of settlements in the Nagada region used hair that had been excavated 60 years earlier. Now researchers have used newer methods
22.12 Pigs and prestige in ancient China. It appears that pigs in Stone Age China were not just a source of food. Owning pigs was also a display of wealth. Evidence for this comes from examining burial sites. If the skulls of sacrificed pigs tend to appear along with expensive ornaments, that
22.11 Diet and bowel cancer. It has long been thought that eating a healthier diet reduces the risk of bowel cancer. A large study cast doubt on this advice. The subjects were 2079 people who had polyps removed from their bowels in the past six months. Such polyps may lead to cancer. The subjects
22.10 Diet and diabetes. Does eating more fiber reduce the blood cholesterol level of patients with diabetes? A randomized clinical trial compared normal and high-fiber diets.Here is part of the researchers’ conclusion: “The high-fiber diet reduced plasma total cholesterol concentrations by 6.7
22.9 Students’ earnings. The financial aid office of a university asks a sample of students about their employment and earnings. The report says, “For academic year earnings, a significant difference (P=0.028) was found between the sexes, with men earning more on average than women. No
22.8 Ethnocentrism. A social psychologist reports, “In our sample, ethnocentrism was significantly higher (P
22.7 Pulse rates. Suppose that a report by a leading medical organization claims that the healthy human heart beats an average of 72 times per minute. Advances in science have led some researchers to question if the healthy human heart beats an entirely different amount of time, on average, per
22.6 Statistical significance. If the results of a statistical test are considered to be statistically significant, what does this mean?a. The results are important.b. The results are not likely to happen just by chance.c. The P-value is large.d. The alternative hypothesis is true.
22.5 College students and the Internet. It is reported that college students spend an average of 100 minutes per day on the Internet. An educational technologist disputes this claim and believes that college students spend more than an average of 100 minutes per day on the Internet. When a random
22.4 Watching the news. In 2018, the Pew Research Center published a report in which it was claimed that 44% of adults in the United States prefer watching the news on television as opposed to reading it or listening to it on the radio. A researcher believes that significantly more than 44% of
21.42 Plus four confidence intervals for a proportion. The large-sample confidence interval p^±z*p^(1−p^)/n for a sample proportion p is easy to calculate. It is also easy to understand because it rests directly on the approximately Normal distribution of p^.Unfortunately, confidence levels from
21.41 A sampling distribution, continued. Exercise 21.39 presents 50 sample means x¯from 50 random samples of size 100. Using a calculator, find the mean and standard error of these 50 values. Then answer these questions.a. The mean of the population from which the 50 samples were drawn is μ=0.5
21.40 Will they charge more? In Exercise 21.38, you carried out the calculations for a confidence interval based on a bank’s experiment in changing the rules for its credit cards.You ought to ask some questions about this study.a. The distribution of the amount charged is skewed to the right, but
21.39 A sampling distribution. Exercise 21.37 concerns the mean of the random numbers generated by a computer program. The mean is supposed to be 0.5 because the numbers are supposed to be spread at random from 0 to 1. We asked the software to generate samples of 100 random numbers repeatedly. Here
21.38 Will they charge more? A bank wonders whether omitting the annual credit card fee for customers who charge at least $2500 in a year will increase the amount charged on its credit cards. The bank makes this offer to an SRS of 200 of its credit card customers. It then compares how much these
21.37 Testing a random number generator. Our statistical software has a “random number generator” that is supposed to produce numbers scattered at random from 0 to 1. If this is true, the numbers generated come from a population with μ=0.5. A command to generate 100 random numbers gives
21.36 Blood pressure. A randomized comparative experiment studied the effect of diet on blood pressure. Researchers divided 54 healthy white males at random into two groups. One group received a calcium supplement, and the other group received a placebo. At the beginning of the study, the
21.35 Averages versus individuals. Scores on the ACT college entrance examination vary Normally with mean μ=18 and standard deviation σ=6. The range of reported scores is 1 to 36.a. What range contains the middle 95% of all individual scores?b. If the ACT scores of 50 randomly selected students
21.34 IQ test scores. Here are the IQ test scores of 31 seventh-grade students in a Midwest school district:114 100 104 89 102 91 114 114 103 105 108 130 120 132 111 128 118 119 86 72 111 103 74 112 107 103 98 96 112 112 93a. We expect the distribution of IQ scores to be close to Normal. Make a
21.33 The idea of a sampling distribution. Figure 21.1 (page 489) shows the idea of the sampling distribution of a sample proportion p^ in picture form. Draw a similar picture that shows the idea of the sampling distribution of a sample mean x¯.
21.32 Safe margin of error. The margin of error z*p^/(1−p^)n is 0 when p^ is 0 or 1 and is largest when p^ is 1/2. To see this, calculate p^(1−p^) for p^ = 0, 0.1, 0.2, . . . , 0.9, and 1.Plot your results vertically against the values of p^ horizontally. Draw a curve through the points. You
21.31 Estimating unemployment. The Bureau of Labor Statistics (BLS) uses 90%confidence in presenting unemployment results from the monthly Current Population Survey(CPS). The November 2018 survey reported that of the 162,770 individuals surveyed in the civilian labor force, 156,795 were employed
21.30 Unhappy HMO patients. How likely are patients who file complaints with a health maintenance organization (HMO) to leave the HMO? In one year, 639 of the more than 400,000 members of a large New England HMO filed complaints. Fifty-four of the complainers left the HMO voluntarily. (That is,
21.29 Restaurant nutrition labels. A 2018 Gallup survey on food labeling found that 45% of a sample of 1033 American adults report paying a great deal or a fair amount of attention to nutritional information that is printed on restaurant menus or posted in restaurants. Use this survey result and
21.28 Using public libraries. Exercise 21.13 reports a 2016 Pew Research Center survey on public library usage in which 768 in a sample of 1601 American adults said that they had visited, in person, a library or bookmobile in the last year. Use Table 21.1 to give a 99%confidence interval for the
21.27 Gun control. Exercise 21.12 reports a Gallup survey in which 697 of a sample of 1041 adults said they wanted stricter laws covering the sale of firearms. Use Table 21.1 to give a 90% confidence interval for the proportion of all adults who feel this way. How does your interval compare with
21.26 Simulating confidence intervals. In Exercise 21.25, you found the recipe for a 68%confidence interval for a population proportion p. Suppose that (unknown to anyone) 20% of college seniors plan to go to graduate or professional school.a. How would you simulate the proportion of an SRS of 25
21.25 68% confidence. We used the 95 part of the 68–95–99.7 rule to give a recipe for a 95% confidence interval for a population proportion p.a. Use the 68 part of the rule to give a recipe for a 68% confidence interval.b. Explain in simple language what “68% confidence” means.c. Use the
21.24 The quick method. The quick method of Chapter 3 (pages 43–44) uses p^±1/n as a rough recipe for a 95% confidence interval for a population proportion. The margin of error from the quick method is a bit larger than needed. It differs most from the more accurate method of this chapter when
21.23 Do you jog? Suppose that 10% of all adults jog. An opinion poll asks an SRS of 400 adults if they jog.a. What is the sampling distribution of the proportion p^ in the sample who jog?b. According to the 68–95–99.7 rule, what is the probability that the sample proportion who jog will be
21.22 Harley motorcycles. In 2013, it was reported that 55% of the new motorcycles that were registered in the United States were Harley-Davidson motorcycles. You plan to interview an SRS of 600 new motorcycle owners.a. What is the sampling distribution of the proportion of your sample who own
21.21 Share the wealth. The New York Times conducted a nationwide poll of 1650 randomly selected American adults. Of these, 1089 felt that the distribution of money and wealth in this country should be more evenly distributed among more people. We can consider the sample to be an SRS.a. Give a 95%
21.20 Count Buffon’s coin. The eighteenth-century French naturalist Count Buffon tossed a coin 4040 times. He got 2048 heads. Give a 95% confidence interval for the proportion of all Buffon’s coin tosses that land head side up. Are you confident that this proportion is not 0.5?Why?
21.19 Don’t forget the basics. Vaping involves inhaling vapors (sometimes including nicotine) from electronic devices. How prevalent is this practice among high school seniors?In 2017, a publication entitled “Monitoring the Future: National Survey Results on Drug Use” reported that of 13,500
21.18 Tossing a thumbtack. If you toss a thumbtack on a hard surface, what is the probability that it will land point up? Estimate this probability p by tossing a thumbtack 100 times. The 100 tosses are an SRS of size 100 from the population of all tosses. The proportion of these 100 tosses that
21.17 Random digits. We know that the proportion of 0s among a large set of random digits is p=0.1 because all 10 possible digits are equally probable. The entries in a table of random digits are a random sample from the population of all random digits. To get an SRS of 200 random digits, look at
21.16 The effect of sample size. A November 2018 CBS News Poll found that 35% of its sample planned to use online retailers for most holiday shopping. Give a 95%confidence interval for the proportion of all adults who plan to shop in this way, assuming that the result p^=0.35 comes from a sample of
21.15 Gun control. In Exercise 21.12, you constructed a 95% confidence interval based on a random sample of n=1041 adults. How large a sample would be needed to get a margin of error half as large as the one in Exercise 21.12? You may find it helpful to refer to the discussion surrounding Example 5
21.14 Computer crime. Adults are spending more and more time on the Internet, and the number experiencing computer-based or Internet-based crime is rising. A 2018 Gallup Poll of 1019 adults, aged 18 and older, found that 723 of those in the sample said that they worry about having their personal,
21.13 Using public libraries. In 2016, the Pew Research Center reported the results of a survey about public library usage. A nationally representative sample of 1601 people ages 16 and older who were living in the United States completed the survey. One survey question asked whether the survey
21.12 Gun control. A March 2018 Gallup survey asked a sample of 1041 adults if they wanted stricter laws covering the sale of firearms. A total of 697 of the survey respondents said “yes.” Although the samples in national polls are not SRSs, they are similar enough that our method gives
21.11 Are teachers engaged in their work? Results from a Gallup survey conducted in 2013 and 2014 reveal that 30% of kindergarten through grade 12 school teachers report feeling engaged in their work. The report from this random sample of 6711 teachers stated that, with 95% confidence, the margin
21.10 Fire the coach? A college president says, “99% of the alumni support my firing of Coach Boggs.” You contact an SRS of 200 of the college’s 15,000 living alumni and find that 66 of them support firing the coach.a. What population does the inference concern here?b. Explain clearly what
21.9 A student survey. Tonya wants to estimate the proportion of the students in her dormitory like the dorm food. She interviews an SRS of 50 of the 175 students living in the dormitory. She finds that 14 think the dorm food is good.a. What population does Tonya want to draw conclusions about?b.
21.8 Pigs. A 90% confidence interval is calculated for a sample of weights of 135 randomly selected pigs, and the resulting confidence interval is from 75 to 90 pounds. Will the sample mean weight (from this particular sample of size 135) fall within the confidence interval?a. Nob. Yesc. Maybe
21.7 Anxiety. A particular psychological test is used to measure anxiety. The average test score for all university students nationwide is 85 points. Suppose a random sample of university students is selected and a confidence interval based on their mean anxiety score is constructed. Which of the
21.6 Computer use. A random sample of 197 12th-grade students from across the United States was surveyed, and it was observed that these students spent an average of 23.5 hours on the computer per week, with a standard deviation of 8.7 hours. If we plan to use these data to construct a 99%
21.5 Barriers to travel. In their 2018 Travel Trends report, the American Association of Retired Persons reported the results of a survey of 374 adults between the ages of 20 and 36 years. Of the 374 individuals in this age group, 176 indicated that cost was the biggest barrier when it comes to
21.4 Gun ownership. In 2017, the Pew Research Center published the results of a survey on gun ownership. A random sample of 3930 American adults aged 18 years and older participated in this survey. Of these 3930 individuals, 1269 individuals reported that they owned at least one gun. Of these
20.28 Casino winnings. What is a secret, at least to naive gamblers, is that in the real world, a casino does much better than expected values suggest. In fact, casinos keep a bit over 20%of the money gamblers spend on roulette chips. That’s because players who win keep on playing. Think of a
20.27 A common expected value. Here is a common setting that we simulated in Chapter 19: there are a fixed number of independent trials with the same two outcomes and the same probabilities on each trial. Tossing a coin, shooting basketball free throws, and observing the sex of newborn babies are
20.26 Repeating an exam. Exercise 19.19 (page 457) gives a model for up to three attempts at an exam in a self-paced course. In that exercise, you simulated 50 repetitions to estimate Elaine’s probability of passing the exam. Use those simulations (or do 50 new repetitions) to estimate the
20.25 A multiple-choice exam. Charlene takes a quiz with 10 multiple-choice questions, each with five answer choices. If she just guesses independently at each question, she has probability 0.20 of guessing right on each. Use simulation to estimate Charlene’s expected number of correct answers.
20.24 Play this game, please. OK, friends, we’ve got a little deal for you. We have a fair coin (heads and tails each have probability 0.5). Toss it twice. If two heads come up, you win right there. If you get any result other than two heads, we’ll give you another chance: toss the coin twice
20.23 We really want a girl. Example 4 estimates the expected number of children a couple will have if they keep going until they get a girl or until they have three children. Suppose that they set no limit on the number of children but just keep going until they get a girl. Their expected number
20.22 An easy A. The distribution of grades in an easy introductory statistics course is as follows:Grade: A B C D F Probability: 0.4 0.3 0.2 0.1 0.0 To calculate student grade point averages, grades are expressed in a numerical scale with A =4, B = 3, and so on down to F = 0.a. Find the expected
20.21 Household size. The Census Bureau gives this distribution for the number of people in American households in 2016:Family size: 1 2 3 4 5 6 7 Proportion: 0.28 0.35 0.15 0.13 0.06 0.02 0.01(Note: In this table, 7 actually represents households of size 7 or greater. But for purposes of this
20.20 Life insurance. You might sell insurance to a 20-year-old friend. The probability that a man aged 20 will die in the next year is about 0.0007. You decide to charge $2000 for a policy that will pay $1 million if your friend dies.a. What is your expected profit on this policy?b. Although you

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