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essentials of statistics

The Basic Practice Of Statistics 5th Edition David S Moore - Solutions

Shaq’s free throws. The basketball player Shaquille O’Neal makes about half of•••APPLET his free throws over an entire season.Use the Probability applet or statistical software to simulate 100 free throws shot by a player who has probability 0.5 of making each shot. (In most software, the
What probability doesn’t say. The idea of probability is that the proportion of•••APPLET heads in many tosses of a balanced coin eventually gets close to 0.5. But does the actual count of heads get close to one-half the number of tosses? Let’s find out. Set the “Probability of heads”
Nickels falling over. You may feel that it is obvious that the probability of a head in tossing a coin is about 1/2 because the coin has two faces. Such opinions are not always correct. Stand a nickel on edge on a hard, flat surface. Pound the surface with your hand so that the nickel falls over.
Playing Pick 4. The Pick 4 games in many state lotteries 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 probability
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 μ = 9 and standard deviation σ = 2.5. An opinion poll asks this question of an SRS of 1100 adults. We will see later that in this situation the sample
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 of the sample who
More random numbers. Find these probabilities as areas under the density curve you sketched in Exercise 10.49.(a) P(0.5 < Y < 1.3)(b) P(Y ≥ 0.8)
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 take any value between 0 and 2. Then the density curve of the outcomes has constant height between 0 and 2, and height 0
Unusual dice. Nonstandard dice can produce interesting 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 distribution for
Birth order. A couple plans to have three children. There are 8 possible arrangements of girls and boys. For example, 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
Who goes to Paris? Abby, Deborah, Mei-Ling, Sam, and Roberto work in a firm’s public relations office. Their employer 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
First digits again. A crook who never heard of Benford’s law might choose the first digits of his faked invoices so that all of 1, 2, 3, 4, 5, 6, 7, 8, and 9 are equally likely. Call the first digit of a randomly chosen fake invoice W for short.(a) Write the probability distribution for the
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 nonword errors has the following
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?
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 (c) and (d) of the previous
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 chosen
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
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.
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 opposite 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 the
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:I0 I0 99 99 77 33 77 99(a) What is the probability that you draw a 9?(b) What is the probability that you draw a red 9?(c)
Car colors. Choose a new car or light truck at random and note its color. Here are the probabilities of the most popular colors for vehicles made in North America in 2007:7 Color White Silver Black Red Gray Blue Probability 0.19 0.18 0.16 0.13 0.12 0.12(a) What is the probability that the vehicle
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 Spanish French German All others None Probability 0.26 0.09 0.03 0.03 0.59(a) Explain why this is a legitimate
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
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 person has a high school diploma but no further education, and 0.30 that the person has at least a bachelor’s degree.(a) What
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 rules of probability. If not, give specific reasons for your answer.(a) Roll a die and record the count of spots on the
Sample space. In each of the following situations, describe 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 baskets she
Choose a common fruit fly Drosophila melanogaster at random. Call the length of the thorax (where the wings and legs attach) Y . The random variable Y has the Normal distribution with mean μ = 0.800 millimeter (mm) and standard deviationσ = 0.078 mm. The probability P(Y > 1) that the fly you
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 ignore the few households that own more than 5 cars:Number of cars X 0 1 2 3 4 5 Probability 0.09 0.36 0.35 0.13 0.05 0.02 A
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
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 a 0?(a) 1/9 (b) 1/10 (c) 9/10
What is the probability that a randomly chosen American does not have type O blood?(a) 0.55 (b) 0.45 (c) 0.04
Maria has type B blood. She can safely receive blood transfusions from people with blood types O and B. What is the probability that a randomly chosen American can donate blood to Maria?(a) 0.11 (b) 0.44 (c) 0.56
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.
This probability model is(a) continuous. (b) discrete. (c) equally likely.
Abasketball 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.Here is the probability model for the blood type of a randomly chosen
You read in a book on poker that the probability of being 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 them
Randomization avoids bias. Suppose that the 25 even-numbered students among APPLET •••the 50 students available for the comparison of on-campus and online instruction(Example 9.5) are older, employed students. We hope that randomization will distribute these students roughly equally between
An herb for depression? Does the herb Saint-John’s-wort relieve major depression?Here are some excerpts from the report of a study of this issue.20 The study concluded that the herb is no more effective than a placebo.(a) “Design: Randomized, double-blind, placebo-controlled clinical trial. . .
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 “antioxidants” such as vitamins A, C, and E. Will taking antioxidants help prevent colon cancer? A medical
Quick randomizing. Here’s a quick and easy way to randomize. You have 100 subjects, 50 women and 50 men. Toss a coin. If it’s heads, assign all the men to the treatment group and all the women to the control group. If the coin comes up tails, assign all the women to treatment and all the men to
Wine, beer, or spirits? Women as a group develop heart disease much later than men. We can improve the completely randomized design of Exercise 9.45 by using women and men as blocks. Your 300 subjects include 120 women and 180 men.Outline a block design for comparing wine, beer, and spirits. Be
Wine, beer, or spirits? There is good evidence that moderate alcohol use improves health. Some people think that red wine is better for your health than other alcoholic drinks. You have recruited 300 adults aged 45 to 65 who are willing to follow your orders about alcohol consumption over the next
Protecting ultramarathon runners. An ultramarathon, as you might guess, is a footrace longer than the 26.2 miles of a marathon. Runners commonly develop respiratory infections after an ultramarathon. Will taking 600 milligrams of vitamin C daily reduce these infections? Researchers randomly
Athletes taking oxygen. We often see players on the sidelines of a football game inhaling oxygen. Their coaches think this will speed their recovery.We might measure recovery from intense exertion as follows: Have a football player run 100 yards three times in quick succession. Then allow three
Growing trees faster. The concentration of carbon dioxide (CO2) in the atmosphere is increasing rapidly 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 researchers to pipe extra CO2 to a
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
Checking the randomization. If the random assignment 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 recording and comparing many such variables, the investigators said
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
Experimental design. The clinical trial was a completely randomized experiment that assigned 240 patients at random among 4 treatments as follows:Antibiotic Placebo pill pill Steroid spray 53 64 Placebo spray 60 63(a) Outline the design of the experiment.(b) How will you label the 240 subjects?(c)
Relieving headaches. Doctors identify “chronic tension-type headaches” as headaches that occur almost daily for at least six months. Can antidepressant medications or stress management training reduce the number and severity of these headaches? Are both together more effective than either
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
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 comparative experiment. The subjects were healthy men aged 35 to 65.They were randomly assigned to drink red wine (9 subjects),
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.”The men earned money by weaving belts. They used their earnings to pay for meals and other consumption and
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 tamperproof time and date stamp and ask a student to take a
Attitudes toward homeless people. Negative attitudes toward poor people are common. Are attitudes 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
Observation versus experiment. Observational studies had suggested that vitamin E reduces the risk of heart disease. 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 category of
Samples versus experiments. Give an example of a question about college students, their behavior, or their opinions that would best be answered by(a) a sample survey.(b) an experiment.
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
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 after
A marketing class designs two videos advertising an expensive Mercedes 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
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.
The Community Intervention Trial for Smoking Cessation asked whether a community-wide advertising campaign would reduce smoking. The researchers located 11 pairs of communities, each pair similar in location, size, economic status, and so on. One community in each pair participated in the
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 labels 01
An important response variable in the experiment described in Exercise 9.21 must be(a) the amount of salt in the subject’s diet.(b) which of the four diets a subject is assigned to.(c) change in blood pressure after 8 weeks on the assigned diet.
In the experiment of the previous exercise, the 240 subjects are labeled 001 to 240.Software assigns an SRS of 60 subjects 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 randomized
Can changing diet reduce high blood pressure? Vegetarian diets and low-salt diets are both promising. Men with high blood pressure are assigned at random to four diets: (1) normal diet with unrestricted salt; (2) vegetarian with unrestricted salt; (3)normal with restricted salt; and (4) vegetarian
What electrical changes occur in muscles as they get tired? Student subjects hold their arms above their shoulders until they have to drop them. Meanwhile, the electrical activity in their arm muscles is measured. This is(a) an observational study.(b) an uncontrolled experiment.(c) a randomized
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
Polling Hispanics. A New York Times News Service article on a poll concerned with the opinions of Hispanics includes this paragraph:The poll was conducted by telephone from July 13 to 27, with 3,092 adults nationwide, 1,074 of whom described themselves as Hispanic. It has a margin of sampling error
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 compare
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.
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 using
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-recent-birthday
Why random digit dialing is common. The list of individuals from which a sample is actually selected is called the sampling frame. Ideally, the frame should list every individual in the population, but in practice this is often difficult.Aframe that leaves out part of the population is a common
Systematic random samples. Systematic random samples go through a list of the population at fixed intervals from a randomly chosen starting point. For example, a study of dating among college students chose a systematic sample of 200 single male students at a university as follows.18 Start with a
Sampling Amazon forests. Stratified samples are widely used to study large areas of forest. Based on satellite images, a forest area in the Amazon basin is divided into 14 types. Foresters studied the four most commercially valuable types: alluvial climax forests of quality levels 1, 2, and 3, and
Sampling at a party. At a large block party there are 290 men and 110 women. You want to ask opinions about how to improve the next party. To be sure that women’s opinions are adequately represented, you decide to choose a stratified random sample of 20 men and 20 women. Explain how you will
Sampling at a party. At a party there are 30 students over age 21 and 20 students under age 21. You choose at random 3 of those over 21 and separately choose at random 2 of those under 21 to interview about attitudes toward alcohol. You have given every student at the party the same chance to be
Seat belt use. A study in El Paso, Texas, looked at seat belt use by drivers. Drivers were observed at randomly chosen convenience stores. After they left their cars, they were invited to answer questions that included questions about seat belt use. In all, 75% said they always used seat belts, yet
Running red lights. The sample described in the previous exercise produced a list of 5024 licensed drivers. The investigators then chose an SRS of 880 of these drivers to answer questions about their driving habits.(a) How would you assign labels to the 5024 drivers? Use Table B, starting at line
Nonresponse. Academic sample surveys, unlike commercial polls, often discuss nonresponse. A survey of drivers began by randomly sampling all listed residential telephone numbers in the United States. Of 45,956 calls to these numbers, 5029 were completed.16 What was the rate of nonresponse for this
Movie viewing. An opinion poll calls 2000 randomly chosen residential telephone numbers, then asks to speak with an adult member of the household. The interviewer asks, “How many movies have you watched in a movie theater in the past 12 months?”(a) What population do you think the poll has in
Random digits. Which of the following statements are true of a table of random digits, and which are false? Briefly explain your answers.(a) There are exactly four 0s in each row of 40 digits.(b) Each pair of digits has chance 1/100 of being 00.(c) The digits 0000 can never appear as a group,
Random digits. In using Table B repeatedly to choose random samples, you should not always begin at the same place, such as line 101. Why not?
Sampling pharmacists. All pharmacists in the Canadian province of Ontario are required to be members of the Ontario College of Pharmacists. The membership list contains 7500 names.(a) How would you label the names in order to select an SRS?(b) Use software or Table B, starting at line 142, to
Sampling the forest. To gather data on a 1200-acre pine forest in Louisiana, the U.S. Forest Service laid a grid of 1410 equally spaced circular plots over a map of the forest. A ground survey visited a sample of 10% of these plots.15(a) How would you label the plots?(b) Choose the first 5 plots in
Sampling telephone area codes. There are approximately 341 active telephone area codes covering Canada, the United States, and some Caribbean areas. (More are created regularly.) You want to choose an SRS of 25 of these area codes for a study of available telephone numbers. Label the codes 001 to
Do you trust the Internet? You want to ask a sample of college students the question “How much do you trust information about health that you find on the Internet—a great deal, somewhat, not much, or not at all?” You try out this and other questions on a pilot group of 10 students chosen from
Sampling stuffed envelopes. A large retailer prepares its customers’ monthly credit card bills using an automatic machine that folds the bills, stuffs them into envelopes, and seals the envelopes for mailing. Are the envelopes completely sealed?Inspectors choose 40 envelopes from the 1000 stuffed
Are you feeling stressed? A Gallup Poll asked, “In general, how often do you experience stress in your daily life—never, rarely, sometimes, or frequently?”Gallup’s report said, “Results are based on telephone interviews with 1,027 national adults, aged 18 and older, conducted Dec. 6–9,
The Gallup Poll asked a random sample of adults, “Do you have enough time to do what you want to do?” In the entire sample, 53% said “No.” But 62% of parents of children younger than age 18 said “No.”Which of these two sample percents will be more accurate as an estimate of the truth
A sample of households in a community is selected at random from the telephone directory. In this community, 4% of households have no telephone, 10% have only cell phones, and another 25% have unlisted telephone numbers. The sample will certainly suffer from(a) nonresponse.(b) undercoverage.(c)
Archaeologists plan to examine a sample of 2-meter-square plots near an ancient Greek city for artifacts visible in the ground. They choose separate samples of plots from floodplain, coast, foothills, and high hills. What kind of sample is this?(a) A simple random sample.(b) A stratified random
You want to choose an SRS of 5 of the 7200 salaried employees of a corporation. You label the employees 0001 to 7200 in alphabetical order. Using line 111 of Table B your sample contains the employees labeled (a) 6694, 5130, 0041, 2712, 3827.(b) 6694, 0513, 0929, 7004, 1271.(c) 8148, 6694, 8760,
You are using the table of random digits to choose a simple random sample of 6 students from a class of 30 students. You label the students 01 to 30 in alphabetical order. Go to line 133 of Table B. Your sample contains the students labeled(a) 45, 74, 04, 18, 07, 65.(b) 04, 18, 07, 13, 02, 07.(c)
You must choose an SRS of 10 of the 440 retail outlets in New York that sell your company’s products. How would you label this population in order to use Table B?(a) 001, 002, 003, . . . , 439, 440(b) 000, 001, 002, . . . , 439, 440(c) 1, 2, . . . , 439, 440
TheWeb portal AOL places opinion poll questions next to many of its news stories.Simply click your response to join the sample. One of the questions in January 2008 was “Do you plan to diet this year?” More than 30,000 people responded, with 68%saying “Yes.”You can conclude that(a) about
A committee on community relations in a college town plans to survey local businesses about the importance of students as customers. From telephone book listings, the committee chooses 150 businesses at random. Of these, 73 return the questionnaire mailed by the committee. The population for this
An opinion poll contacts 1161 adults and asks them, “Which political party do you think has better ideas for leading the country in the twenty-first century?”In all, 696 of the 1161 say, “The Democrats.”The sample in this setting is(a) all 235 million adults in the United States.(b) the
Python eggs. How is the hatching of water python eggs influenced by the temper-ature of the snake’s nest? Researchers placed 104 newly laid eggs in a hot environment, 56 in a neutral environment, and 27 in a cold environment. Hot duplicates the warmth provided by the mother python. Neutral and

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