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essential statistics

Essential Statistics 1st Edition David S Moore - Solutions

10.6 Measurements in the lab. Juan makes a measurement in a chemistry laboratory and records the result in his lab report. The standard deviation of students' lab measurements is CT= 10 milligrams. Juan repeats the measurement 3 times and records the mean x of his 3 measurements.(a) What is the
10.5 Generating a sampling distribution. Let's illustrate the idea of a sampling distribution in the case of a very small sample from a very small population. The population is the scores of 10 students on an exam;Student Score 082 162 280 358 472 573 665 766 74 962 The parameter of interest is the
10.4 Sampling distribution versus population distribution. During World War II, 12,000 able-bodied male undergraduates at the University of Illinois participated in required physical training. Each student ran a timed mile. Their times followed the Normal dis tribution with mean 7.11 minutes and
10.2 Florida voters. Florida has played a key role in recent presidential elections. Voter registration records show that 41% of Florida voters are registered as Democrats and 37% as Republicans. (Most of the others did not choose a party.) To test a random digit dialing device, you use it to call
10.1 Effects of caffeine. How does caffeine affect our bodies ? In a matched pairs experiment, subjects pushed a button as quickly as they could after taking a caffeine pill and also after taking a placebo pill. The mean pushes per minute were 283 for the placebo and 311 for caffeine. Is each of
9.47 Playing Pick 4. The Pick 4 games in many state lotter ies announce a four-digit winning number each day. Each of the 10,000 possible numbers 0000 to 9999 has the same chance of winning. You win if your choice matches the winning digits.Suppose your chosen number is 5974.(a) What is the
9.46 Unusual dice. Nonstandard dice can produce interest ing distributions of outcomes. You have two balanced, six-sided dice. One is a standard die, with faces having 1, 2, 3, 4, 5, and 6 spots. The other die has three faces with 0 spots and three faces with 6 spots. Find the probability
9.45 Friends. How many close friends do you have? Suppose that the number of close friends adults claim to have varies from person to person with mean /r = 9 and standard devia tion cr = 2.5. An opinion poll asks this question of an SRS of 1100 adults. We will see later that in this situation the
9.44 Did you vote? A sample survey contacted an SRS of 663 registered voters in Oregon shortly after an election and asked respondents whether they had voted. Voter records show that 56% of registered voters had actually voted. We will see later that in this situation the proportion ot the sample
9.43 More random numbers. Find these probabilities as ar eas under the density curve you sketched in Exercise 9.42.(a) P(0.5 < Y < 1.3)(b) P(Y > 0.8)
9.42 Random numbers. Many random number generators allow users to specify the range of the random numbers to be produced. Suppose that you specify that the random number Y can rake any value between 0 and 2. Then the density curve of the outcomes has constant height between 0 and 2, and height 0
9.41 Birth order. A couple plans to have three children.There are 8 possible arrangements of girls and boys. For exam ple, GGB means the first two children are girls and the third child is a boy. All 8 arrangements are (approximately) equally likely.(a) Write down all 8 arrangements of the sexes of
9.40 Who goes to Paris? Abby, Deborah, Mei-Ling, Sam, and Roberto work in a firm's public relations office. Their em ployer must choose two of them to attend a conference in Paris.To avoid unfairness, the choice will be made by drawing two names from a hat. (This is an SRS of size 2.)(a) Write down
9.39 First digits again. A crook who never heard of Benford's law might fake invoices so that the first digits of the amounts are equally likely to be any of 1, 2, 3, 4, 5, 6, 7, 8, or 9. Call the first digit of a randomly chosen fake invoice W for short.(a) Write the probability distribution for
9.38 Spelling errors. Spell-checking software catches "nonword errors" that result in a string of letters that is not a word, as when "the" is typed as "teh." When undergraduates are asked to type a 250-word essay (without spell-checking), the number X of ironword errors has the following
9.37 Where do young people live, continued.(a) What is the probability that the person chosen is 21 years old or older?(b) What is the probability that the person chosen does not live with his or her parents?
9.36 Where do young people live, continued.(a) List the outcomes that make up the event A = {The person chosen is either 19 years old or lives in his or her own place, or both}(b) What is P (A) ? Explain carefully why P (A) is not the sum of the probabilities you found in parts (b) and (c) of the
9.35 Where do young people live?(a) Why is this a legitimate discrete probability model?(b) What is the probability that the person chosen is a 19-year-old who lives in his or her own place?(c) What is the probability that the person is 19 years old?(d) What is the probability that the person
9.34 Race and ethnicity. The Census Bureau allows each person to choose from a long list of races. That is, in the eyes of the Census Bureau, you belong to whatever race you say you belong to. "Hispanic/Latino" is a separate category; Hispanics may be of any race. If we choose a resident of the
9.33 A door prize. A party host gives a door prize to one guest chosen at random. There are 48 men and 42 women at the party. What is the probability that the prize goes to a woman?Explain how you arrived at your answer.
9.32 Loaded dice. There are many ways to produce crooked dice. To load a die so that 6 comes up too often and 1 (which is opjjosite 6) comes up too seldom, add a bit of lead to the filling of the spot on the 1 face. If a die is loaded so that 6 comes up with probability 0.2 and the probabilities of
9.31 Drawing cards. You are about to draw a card at random(that is, all choices have the same probability) from a set of 7 cards. Although you can't see the cards, here they are:(a) What is the probability that you draw a 9?(b) What is the probability that you draw a red 9?(c) What is the
9.30 Car colors. Choose a new car or light truck at random and note its color. Here are the probabilities of the most popu lar colors for vehicles made in North America in 2007:'Color Probability White 0.19 Silver 0.18 Black 0.16 Red 0.13 Gray 0.12 Blue 0.12(a) What is the probability that the
9.29 Foreign-language study. Choose a student in grades 9 to 12 at random and ask if he or she is studying a language other than English. Here is the distribution of results:Language Probability Spanish French 0.26 0.09 German All others None 0.03 0.03 0.59(a) Explain why this is a legitimate
9.28 Land in Canada. Canada's national statistics agency.Statistics Canada, says that the land area of Canada is 9,094,000 square kilometers. Of this land, 4,176,000 square kilometers are forested. Choose a square kilometer of land in Canada at random.(a) What is the probability that the area you
9.27 Education among young adults. Choose a young adult (aged 25 to 29) at random. The probability is 0.13 that the person chosen did not complete high school, 0.29 that the petson has a high school diploma but no further education, and 0.30 that the person has at least a bachelor's degree.(a) What
9.26 Probability models? In each of the following situations, state whether or not the given assignment of probabilities to individual outcomes is legitimate, that is, satisfies the tules of probability. If not, give specific reasons for your answer.(a) Roll a die and record the count of spots on
9.25 Sample space. In each of the following situations, desctibe a sample space S for the random phenomenon.(a) A basketball player shoots four free throws. You record the sequence of hits and misses.(b) A basketball player shoots four free throws. You record the number of ba,skets she makes.
9.24 Choose a common fruit fly Drosophila melanogaster at ran dom. Call the length of the thorax (where the wings and legs attach) Y. The random variable Y has the Normal distribu tion with mean /i — 0.800 millimeter (mm) and standard de viation cr = 0.078 mm. The probahility P(Y > 1) that the
9.23 Choose an American household at random and let the random variable X be the number of cars (including SUVs and light trucks) they own. Here is the probability model if we ig nore the few households that own more than 5 cars:Number of cars X Probability _0^0.09 10.36 20.35 3_ 0.13 0.05 _5_ 0.02
9.22 In a table of random digits such as Table B, each digit is equally likely to be any of 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9. What is the probability that a digit in the table is 7 or greater?(a) 7/10 (b) 4/10 (c) 3/10
9.21 The probability that a randomly chosen American has type AB blood must be(a) any number between 0 and 1. (b) 0.04. (c) 0.4.
9.20 Here is the probability model for the blood type of a ran domly chosen person in the United States:Blood type O A B AB Probability 0.45 0.40 0.11 7 This probability model is (a) continuous. (b) discrete. (c) equally likely.
9.19 A basketball player shoots 8 free throws during a game.The sample space for counting the number she makes is(a) S = any number between 0 and 1.(b) S = whole numbers 0 to 8.(c) S = all sequences of 8 hits or misses, like HMMHHHMH.
9.18 You read in a book on poker that the probability of be ing dealt three of a kind in a five-card poker hand is 1/50. This means that(a) if you deal thousands of poker hands, the fraction of them that contain three of a kind will be very close to 1/50.(b) if you deal 50 poker hands, exactly 1 of
9.17 Running a mile. A study of 12,000 able-bodied male students at the University of Illi nois found that their times for the mile run were approximately Normal with mean 7.11 minutes and staiadard deviation 0.74 minute.^ Choose a student at random from this group and call his time for the mile
9.16 Grades in a statistics course. North Carolina State University posts the grade dis tributions for its courses online.^ Students in Statistics 101 in the fall |2007 semester received 26% A's, 42% B's, 20% C's, 10% D's, and 2% F's. Choose a Statistics 101 stu dent at random. To "choose at
9.15 Iowa Test scores. The Normal distribution with mean fx = 6.8 and standard devia tion
9.14 Adding random numbers. Generate two random rmmbers between 0 and 1 and take X to be their sum. The sum X can take any value between 0 and 2. The density curve of X is the triangle shown in Figure 9.7.(a) Verify by geometry that the area under this curve is 1.(b) What is the probability that X
9.13 Random numbers. Let Y be a random number between 0 and 1 produced by the idealized random number generator described in Example 9.7 and Figure 9.4. Find the following probabilities:(a) P(y < 0.4)(b) P(Y < 0.4)(c) P(0.3 < Y
9.12 Working out. Choose a person aged 19 to 25 years at random and ask, "In the past seven days, how many times did you go to an exercise or fitness center or work out?" Call the response X for short. Based on a large sample survey, here is a probability model for the answer you will get:''Days 0
9.11 Benford's law. The first digit of a randomly chosen expense account claim follows Benford's law (Example 9.6). Consider the events A = {first digit is 7 or greater}B = {first digit is odd}(a) What outcomes make up the event A? What is P (A)?(b) What outcomes make up the event B? What is
9.10 Rolling a die. Figure 9.3 displays several discrete probability models for rolling a die.We can learn which model is actually accurate for a particular die only by rolling the die many times. However, some of the models are not legitimate. That is, they do notobey the rules. Which are
9.9 Languages in Canada. Canada has two official languages, English and French. Choose a Canadian at random and ask, "What is your mother tongue?" Here is the distribution of responses, combining many separate languages from the broad Asia/Pacific region:^Language i English French Asian/Pacific
9.8 Overweight? Although the rules of probability are just basic facts about percents or pro portions, we need to be able to use the language of events and their probabilities. Choose an American adult at random. Define two events:A = the person chosen is obese B = the person chosen is overweight,
9.7 Preparing for the GMAT. In many settings, the "rules of probability" are just basic facts about percents. A company that offers courses to prepare students for the Graduate Man agement Admission Test (GMAT) has the following information ahout its customers:20% are currently undergraduate
9.6 Role-playing games. The intelligence of a character in a game is determined by rolling the four-sided die twice and adding 1 to the sum of the spots. Start with your work in the previous exercise to give a probability model (sample space and prob abilities of outcomes) for the character's
9.5 Role-playing games. Computer games in which the players take the roles of characters go back to earlier tabletop games such as Dungeons St Dragons. These games use many different types of dice. A four-sided die has faces with 1, 2, 3, and 4 spots.(a) What is the sample space for rolling a
9.4 Sample space. Choose a student at random from a large statistics class. Describe a sample space S for each of the following. (In some cases you may have some freedom in specify ing S.)(a) Is the student male or female?(b) What is the student's height in inches?(c) Ask how much money in coins
9.3 Random digits. The table of random digits (Table B) was produced by a random mecha nism that gives each digit probability 0.1 of being a 0. So random digits can illustrate the idea of probability.(a) Count the number of Os in each of the first 5 rows of Table B. Each row has 40 digits.What are
9.2 Probability says... Probability is a measure of how likely an event is to occur. Match one of the prohahilities that follow with each statement of likelihood given. (The prohahility is usually a more exact measure of likelihood than is the verbal statement.)0 0.01 0.3 0.6 0.99 1(a) This event
9.1 Texas hold 'em. In the popular Texas hold 'em variety of poker, players make their best five-card picker hand by combining the two cards they are dealt with three of five cards available to all players. You read in a hook on poker that if you hold a pair (two cards of the same rank) in your
8.42 An herb for depression? Does the herb Saint-John'swort relieve major depression? Here are some excerpts from the report of a study of this issue.'® The study concluded that the herb is no more effective than a placebo.(a) "Design: Randomized, double-blind, placebo-controlled clinical trial "A
8.41 Do antioxidants prevent cancer? People who eat lots of fruits and vegetables have lower rates of colon cancer than those who eat little of these foods. Fruits and vegetables are rich in "antioSxidants" such as vitamins A, C, and E. Will tak ing antioxidants help prevent colon cancer? A medical
8.40 Athletes taking oxygen. We often see players on the sidelines of a football game inhaling oxygen. Their coaches think this wiljl speed their recovery. We might measure recov ery from intense exertion as follows: Have a football player run 100 yards three times in quick succession. Then allow
8.39 Growing trees faster. Carbon dioxide (CO2) in the at mosphere is increasing due to our use of fossil fuels. Because green plants use CO2 to fuel photosynthesis, more CO2 may cause trees to grow faster. An elaborate apparatus allows re searchers to pipe extra CO2 to a 30-meter circle of forest.
8.38 Frappuccino light? Here's the opening of a Starbucks press release: "Starbucks Corp. on Monday said it would roll out a line of blended coffee drinks intended to tap into the growing popularity of reduced-calorie and reduced-fat menu choices for Americans." You wonder if Starbucks customers
8.37 Checking the randomization. If the random assign ment of patients to treatments did a good job of eliminating bias, possible lurking variables such as smoking history, asthma, and hay fever should be similar in all 4 groups. After record ing and comparing many such variables, the investigators
8.36 Describing the design. The report of this study in the Journal of the American Medical Association describes it as a"double-bLind, randomized, placebo-controlled factorial trial.""Factorial" means that the treatments are formed from more than one factor. What are the factors? What do
8.35 Experimental design. The clinical trial was a com pletely randomized experiment that assigned 240 patients at random among 4 treatments as follows:Antibiotic pill Placebo pill Steroid spray Placebo spray 53 60 64 63(a) Outline the design of the experiment.(b) How will you label the 240
8.34 Relieving headaches. Can antidepressant medications or stress management training reduce the number and severity of chronic headaches? Are both together more effective than either alone?(a) Use a diagram like Figure 8.2 to display the treatments in a design with two factors: "medication, yes
8.33 Fabric finishing. A maker of fabric for clothing is setting up a new line to "finish" the raw fabric. The line will use either metal rollers or natural-bristle rollers to raise the surface of the fabric; a dyeing cycle time of either 30 minutes or 40 minutes;and a temperature of either 150°C
8.32 The benefits of red wine. Some people think that red wine protects moderate drinkers from heart disease better than other alcoholic beverages. This calls for a randomized compara tive experiment. The subjects were healthy men aged 35 to 65.They were randomly assigned to drink red wine (9
8.31 Marijuana and work. How does smoking marijuana affect willingness to work? Canadian researchers persuaded young adult men who used marijuana to live for 98 days in a "planned environment." One group smoked two potent marijuana cigarettes every evening. The other group smoked two weak marijuana
8.30 Getting teachers to come to school. Elementary schools in rural India are usually small, with a single teacher.The teachers often fail to show up for work. Here is an idea for improving attendance: give the teacher a digital camera with a tamper-proof time and date stamp and ask a student to
8.29 Attitudps toward homeless people. Are attitudes to ward poor people more negative when a person is homeless? To find out, read, to subjects a description of a poor person. There are two versions. One begins Jim is a 30-year'old single man. He is currently living in a small single-room
8.28 Observation versus experiment. Observational stud ies had suggested that vitamin E reduces the risk of heart dis ease. Careful experiments, however, showed that vitamin E has no effect. According to a commentary in the Journal of the American Medical Association:Thus, vitamin E enters the
8.27 Samples versus experiments. Give an example of a question about college students, their behavior, or their opin ions that would best be answered by(a) a sample purvey.(b) an experiment.
8.26 Reducing nonresponse. How can we reduce the rate of refusals in telephone surveys? Most people who answer at all listen to the interviewer's introductory remarks and then decide whether to continue. One study made telephone calls to randomly selected households to ask opinions about the next
8.25 Alcohol and heart attacks. Many studies have found that people who drink alcohol in moderation have lower risk of heart attacks than either nondrinkers or heavy drinkers. Does alcohol consumption also improve survival after a heart attack? One study followed 1913 people who were hospitalized
8.24 A marketing class designs two videos advertising a Mer- cedes sports car. They test the videos by asking fellow students to view both (in random order) and say which makes them more likely to buy the car. Mercedes should be reluctant to agree that the video favored in this study will sell more
8.23 To decide which community in each pair in the previous exercise should get the advertising campaign, it is best to (a) toss a coin. (b) choose the community that will help pay for the campaign. (c) choose the community with a mayor who will participate.
8.22 The Community Intervention Trial for Smoking Cessa- tion asked whether a community-wide advertising campaign would reduce smoking. The researchers located 11 pairs of com- munities, each pair similar in location, size, economic status,and so on. One community in each pair participated in the
8.21 A medical experiment compares an antidepression medicine with a placebo for relief of chronic headaches. There are 36 headache patients available to serve as subjects. To choose 18 patients to receive the medicine, you would (a) assign labels 01 to 36 and use Table B to choose 18. (b) assign
8.20 In the experiment of the previous exercise, the 240 sub- jects are labeled 001 to 240. Software assigns an SRS of 60 sub- jects to Diet 1, an SRS of 60 of the remaining 180 to Diet 2, and an SRS of 60 of the remaining 120 to Diet 3. The 60 who are left get Diet 4. This is a (a) completely
8.19 Can changing diet reduce high blood pressure? Vegetar- ian diets and low-salt diets are both promising. Men with high blood pressure are assigned at random to four diets: (1) nor- mal diet with unrestricted salt; (2) vegetarian with unrestricted salt; (3) normal with restricted salt; and (4)
8.18 The Nurses' Health Study has interviewed a sample of more than 100,000 female registered nurses every two years since 1976. The study finds that "light-to-moderate drinkers had a significantly lower risk of death" than either nondrinkers or heavy drinkers. The Nurses' Health Study is (a) an
8.17 How long did I work? A psychologist wants to know if the difficulty of a task influences our estimate of how long we spend working at it. She designs two sets of mazes that subjects can work through on a computer. One set has easy mazes and the other has hard mazes. Subjects work until told to
8.16 Comparing hand strength. Is the right hand generally stronger than the left in righthanded people? You can crudely measure hand strength by placing a bathroom scale on a shelf with the end protruding, then squeezing the scale between the thumb below and the four fingers above it. The reading
8.15 Does meditation reduce anxiety? An experiment that claimed to show that med itation reduces anxiety proceeded as follows. The experimenter interviewed the sub jects and rated their level of anxiety. Then the subjects were randomly assigned to two groups. The experimenter taught one group how
8.14 Testosterone for older men. As men age, their testosterone levels gradually decrease.This may cause a reduction in lean body mass, an increase in fat, and other unde sirable changes. Do testosterone supplements reverse some of these effects? A study in the Netherlands assigned 237 men aged 60
8.13 Arsenic and lung cancer. Arsenic is frequently found both in the natural environment and in food. A study of the relationship between arsenic in drinking water and deaths from lung cancer measured arsenic levels in drinking water in 138 villages in Taiwan and examined death certificates to
8.12 Conserving energy. Example 8.6 describes an experiment to learn whether provid ing households with digital displays or charts will reduce their electricity consumption.An executive of the electric company objects to including a control group. He says: "It would be simpler to just compare
8.11 Prayer and meditation. You read in a magazine that "nonphysical treatments such as meditation and prayer have been shown to be effective in controlled scientific studies for such ailments as high blood pressure, insomnia, ulcers, and asthma." Explain in sim ple language what the article means
8.10 Effects of TV advertising. Figure 8.2 (page 148) displays the 6 treatments for the twofactor experiment on TV advertising described in Example 8.3. The 36 students named below will serve as subjects. Outline the design and randomly assign the subjects to the 6 treatments. If you use Table B,
8.9 More rain for California? The changing climate will probably bring more rain to California, but we don't know whether the additional rain will come during the win ter wet season or extend into the long dry season in spring and summer. Kenwyn Suttle of the University of California at Berkeley
8.8 Evaluating your own performance. Undergraduate music students often don't eval uate their own performances accurately. Can small-group discussions help? The subjects were 29 students preparing for an end-of-semester performance. Assign 15 students to the treatment: videotape a practice
8.7 Reducing unemployment. Will cash bonuses speed the return to work of unemployed people? A state department of labor notes that last year 68% of people who filed claims for unemployment insurance found a new job within 15 weeks. As an experiment, the state offers $500 to people filing
8.6 Exercise and heart rate. A student project measured the increase in the heart rates of fellow students when they stepped up and down for three minutes to the beat of a metronome. The step was either 5.75 inches or 11.5 inches high and the metronome beat was either 14, 21, or 28 steps per
8.5 Growing In the shade. Ability to grow in shade may help pities in the dry forests of Arizona resist drought. How well do these pines grow in shade? Plant pine seedlings in a greenhouse in either full light, light reduced to 25% of normal by shade cloth, or light reduced to 5% of normal. At the
8.4 Ginkgo extract and the post-lunch dip. The post-lunch dip is the drop in mental alertness after a midday meal. Does an extract of the leaves of the ginkgo tree reduce the post-lunch dip? Assign healthy people aged 18 to 40 to take either ginkgo extract or a placebo pill. After lunch, ask them
8.3 Effects of binge drinking. A common definition of "binge drinking" is 5 or more drinks at one setting for men, aiad 4 or more for women. An observational study finds that stu dents who binge have lower average GPA than those who don't. Suggest some lurking variables that may be confounded witb
8.2 Teaching economics. An educational software company wants to compare the effec tiveness of its computer anirnation for teaching about supply and demand curves with that of a textbook presentation. The company tests the economic knowledge of a number of first-year college students, then divides
8.1 Cell phones and brain cancer. A study of cell phones and the risk of brain cancer looked at a group of 469 people who have brain cancer. The investigators matched each cancer patient with a person of the same sex, age, and race who did not have brain cancer, then asked about use of cell
7.41 Polling HIspanlcs. A New York Times News Service ar ticle on a poll concerned with the opinions of Hispanics in cludes this paragraph:The poll was conducted by telephone from July 13 to 27, with 3,092 adults nationwide, 1,074 of whom de scribed themselves as Hispanic. It has a margin of sam
7.40 Canada's national health care. The Ministry of Health in the Canadian province of Ontario wants to know whether the national health care system is achieving its goals in the province. Much information about health care comes from patient records, but that source doesn't allow us to com pare
7.39 Your own bad questions. Write your own examples of bad sample survey questions.(a) Write a biased question designed to get one answer rather than another.(b) Write a question to which many people may not give truthful answers.
7.38 Wording survey questions. Comment on each of the following as a potential sample survey question. Is the question clear? Is it slanted toward a desired response?(a) "Some cell phone users have developed brain cancer.Should all cell phones come with a warning label explaining the danger of
7.37 Regulating guns. The National Gun Policy Survey asked respondents' opinions about government regulation of firearms. A report from the survey says, "Participating households were identified through random digit dialing; the respondent in each household was selected by the most-recentbirthday
7.36 Systematic random samples. Systematic random sam ples go through a list of the population and choose individuals at fixed intervals from a randomly chosen starting point. For example, a study of dating among college students chose a sys tematic sample of 200 single male students at a

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