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essentials of statistics
The Basic Practice Of Statistics 5th Edition David S Moore - Solutions
Rolling a die. Figure 10.3 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 not obey the rules. Which are legitimate
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:2 Language English French Asian/Pacific Other
Overweight? Although the rules of probability are just basic facts about percents or proportions, 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, but not
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 Management Admission Test (GMAT) has the following information about its customers: 20% are currently undergraduate
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 probabilities of outcomes) for the character’s
Role-playing games. Computer games in which the players take the roles of characters are very popular. They go back to earlier tabletop games such as Dungeons&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
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 specifying S.)(a) Is the student male or female?(b) What is the student’s height in inches?(c) Ask how much money in coins (not
The long run but not the short run. Our intuition about chance behavior is not APPLET ••• very accurate. In particular, we tend to expect that the long-run pattern described by probability will show up in the short run as well. For example, we tend to think that tossing a coin 20 times will
Random digits. The table of random digits (Table B) was produced by a random APPLET ••• mechanism that gives each digit probability 0.1 of being a 0.(a) What proportion of the first 50 digits in the table are 0s? This proportion is an estimate, based on 50 repetitions, of the true
Probability says . . . Probability is a measure of how likely an event is to occur.Match one of the probabilities that follow with each statement of likelihood given.(The probability 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 is
Texas hold ’em. In the popular Texas hold ’em variety of poker, players make their best five-card poker hand by combining the two cards they are dealt with three of five cards available to all players. You read in a book on poker that if you hold a pair (two cards of the same rank) in your
Technology for teaching statistics. The Brigham Young University statistics department is performing randomized comparative experiments to compare teaching methods. Response variables include students’ final-exam scores and a measure of their attitude toward statistics. One study compares two
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 stop
Comparing hand strength. Is the right hand generally stronger than the left in right-handed 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 of
Does meditation reduce anxiety? An experiment that claimed to show that meditation reduces anxiety proceeded as follows. The experimenter interviewed the subjects and rated their level of anxiety. Then the subjects were randomly assigned to two groups. The experimenter taught one group how to
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 undesirable changes. Do testosterone supplements reverse some of these effects? A study in the Netherlands assigned 237 men aged 60 to 80
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 identify
Conserving energy. Example 9.6 describes an experiment to learn whether providing 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
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 simple language what the article means by
Effects of TV advertising. Figure 9.2 (page 227) displays the 6 treatments for the two-factor experiment on TV advertising described in Example 9.3. 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, start
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 winter wet season or extend into the long dry season in spring and summer. Kenwyn Suttle of the University of California at Berkeley and
Evaluating your own performance. Undergraduate music students often don’t evaluate their own performances accurately. Can small-group discussions help? The subjects were 29 students preparing for the end-of-semester performance that is an important part of their grade. Assign 15 students to the
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 unemployment
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 minute.
Growing in the shade. Ability to grow in shade may help pines found 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
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 to
Effects of binge drinking. A common definition of “binge drinking” is 5 or more drinks at one setting for men, and 4 or more for women. An observational study finds that students who binge have lower average GPA than those who don’t. Suggest some lurking variables that may be confounded with
Teaching economics. An educational software company wants to compare the effectiveness of its computer animation 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 them
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 phones.2
Let’s go polling. Use Google or your favorite search engine to search the Web for “web polling software.” Choose one of the sites that offer software that allows you to conduct your own online opinion polls. (At the time of writing, www.pollmonkey.com was a favorite, but things change quickly
Question wording. In 2000, when the federal budget showed a large surplus, the Pew Research Center asked two questions of random samples of adults. Both questions stated that Social Security would be “fixed.” Here are two questions about using the remaining surplus:Question A: Should the money
Ring-no-answer. A common form of nonresponse in telephone surveys is “ringno-answer.” That is, a call is made to an active number but no one answers. The Italian National Statistical Institute looked at nonresponse to a government survey of households in Italy during the periods January 1 to
Academic dishonesty.Astudy of academic dishonesty among college students used a two-stage sampling design. The first stage chose a sample of 30 colleges and universities.Then the study authors mailed questionnaires to a stratified sample of 200 seniors, 100 juniors, and 100 sophomores at each
Sampling metro Chicago. Cook County, Illinois, has the second-largest population of any county in the United States (after Los Angeles County, California). Cook County has 30 suburban townships and an additional 8 townships that make up the city of Chicago. The suburban townships are Barrington Elk
Sampling Pentecostals. Pentecostals are among the fastest-growing Christian groups in many countries. The Pew Forum on Religion and Public Life surveyed Pentecostal Christians in 10 countries and compared their opinions with those of the general population. In South Korea, random samples by Gallup
Ask more people. Just before a presidential election, a national opinion-polling firm increases the size of its weekly sample from the usual 1500 people to 4000 people. Why do you think the firm does this?
Sampling gravestones. The local genealogical society in Coles County, Illinois, has compiled records on all 55,914 gravestones in cemeteries in the county for the years 1825 to 1985. Historians plan to use these records to learn about African Americans in Coles County’s history. They first choose
Minority managers. A firm wants to understand the attitudes of its minority managers toward its system for assessing management performance. Below is a list of all the firm’s managers who are members of minority groups. Use the Simple Random Sample applet, other software, or Table B at line 139
Apartment living. You are planning a report on apartment living in a college town.You decide to select three apartment complexes at random for in-depth interviews with residents. Use the Simple Random Sample applet, other software, or Table B to select a simple random sample of three of the
More sampling on campus. Your college wants to gather student opinion about parking for students on campus. It isn’t practical to contact all students.(a) Give an example of a way to choose a sample of students that is poor practice because it depends on voluntary response.(b) Give another
Sampling on campus. You see a woman student standing in front of the student center, now and then stopping other students to ask them questions. She says that she is collecting student opinions for a class assignment. Explain why this sampling method is almost certainly biased.
Customer satisfaction. A department store mails a customer satisfaction survey to people who make credit card purchases at the store. This month, 45,000 people made credit card purchases. Surveys are mailed to 1000 of these people, chosen at random, and 137 people return the survey form. What is
Student archaeologists. An archaeological dig turns up large numbers of pottery shards, broken stone implements, and other artifacts. Students working on the project classify each artifact and assign it a number. The counts in different categories are important for understanding the site, so the
Sampling students. A political scientist wants to know how college students feel about the Social Security system. She obtains a list of the 3456 undergraduates at her college and mails a questionnaire to 250 students selected at random. Only 104 questionnaires are returned.(a) What is the
Which hospital is safer? To help consumers make informed decisions about health care, the government releases data about patient outcomes in hospitals. You want to compare Hospital A and Hospital B, which serve your community. The table presents data on all patients undergoing surgery in a recent
Airline flight delays. Here are the numbers of flights on time and delayed for two airlines at five airports in one month. Overall on-time percents for each airline are often reported in the news. The airport that flights serve is a lurking variable that can make such reports misleading.5 Alaska
Marginal distributions aren’t the whole story. Here are the row and column totals for a two-way table with two rows and two columns:a b 50 c d 50 60 40 100 Make up two different sets of countsa, b,c, and d for the body of the table that give these same totals. This shows that the relationship
Undergraduates’ ages. Exercise 6.2 gives Census Bureau data describing the age ST EP and sex of all American college undergraduates. We suspect that the percent of women is higher among older students than in the traditional 18 to 24 college age group. Do the data support this suspicion? Follow
Attitudes toward recycled products. Exercise 6.1 gives data on the opinions of people who have and have not bought coffee filters made from recycled paper. To see the relationship between opinion and experience with the product, find the conditional distributions of opinion (the response variable)
Undergraduates’ ages. Here is a two-way table of Census Bureau data describing the age and sex of all American undergraduate college students. The table entries are counts in thousands of students.3 Age group Female Male 15 to 17 years 116 61 18 to 24 years 5470 4691 25 to 34 years 1319 824 35
Attitudes toward recycled products. Recycling is supposed to save resources.Some people think recycled products are lower in quality than other products, a fact that makes recycling less practical. Here are data on attitudes toward coffee filters made of recycled paper among people who had bought
To earn more, get married? Data show that men who are married, and also divorced or widowed men, earn quite a bit more than men the same age who have never been married. This does not mean that a man can raise his income by getting married, because men who have never been married are different from
Education and income. There is a strong positive association between workers’ education and their income. For example, the Census Bureau reports that the median income of young adults (ages 25 to 34) who work full-time increases from $19,956 for those with less than a ninth-grade education, to
Another reason not to smoke?Astop-smoking booklet says, “Children of mothers who smoked during pregnancy scored nine points lower on intelligence tests at ages three and four than children of nonsmokers.”Suggest some lurking variables that may help explain the association between smoking during
Is math the key to success in college? A College Board study of 15,941 high school graduates found a strong correlation between how much math minority students took in high school and their later success in college. News articles quoted the head of the College Board as saying that “math is the
The endangered manatee. Table 4.1 gives 30 years of data on boats registered in Florida and manatees killed by boats. Figure 4.2 (page 102) shows a strong positive linear relationship. The correlation is r = 0.953.(a) Find the equation of the least-squares line for predicting manatees killed from
Outsourcing by airlines. Exercise 4.5 (page 99) gives data for 14 airlines on the percent of major maintenance outsourced and the percent of flight delays blamed on the airline.(a) Make a scatterplot with outsourcing percent as x and delay percent as y. Hawaiian Airlines is a high outlier in the y
Do heavier people burn more energy? Return to the data of Exercise 5.4 (page 132) on body mass and metabolic rate.We will use these data to illustrate influence.(a) Make a scatterplot of the data that is suitable for predicting metabolic rate from body mass, with two new points added. Point A: mass
Influence in regression. The Correlation and Regression applet allows you to animate Figure 5.8. Click to create a group of 10 points in the lower-left corner of the scatterplot with a strong straight-line pattern (correlation about 0.9). Click the “Show least-squares line” box to display the
Does fast driving waste fuel? Exercise 4.8 (page 102) gives data on the fuel consumption y of a car at various speeds x. Fuel consumption is measured in liters of gasoline per 100 kilometers driven, and speed is measured in kilometers per hour.Software tells us that the equation of the
Residuals by hand. In Exercise 5.3 you found the equation of the least-squares line for predicting the number of days y until gorillas in a social group begin to die in an Ebola virus epidemic from the “distance” x from the first group infected.(a) Use the equation to obtain the 6 residuals
Growing corn. Exercise 4.32 (page 118) gives data from an agricultural experiment.The purpose of the study was to see how the yield of corn changes as we change the planting rate (plants per acre).(a) Make a scatterplot of the data. (Use a scale of yields from 100 to 200 bushels per acre.) Find the
How useful is regression? Figure 4.8 (page 114) displays the relationship between golfers’ scores on the first and second rounds of the 2007 Masters Tournament. The correlation is r = 0.192. Exercise 4.30 gives data on solar radiation (SRD) and concentration of dimethylsulfide (DMS) over a region
Ebola and gorillas. An outbreak of the deadly Ebola virus in 2002 and 2003 killed 91 of the 95 gorillas in 7 home ranges in the Congo. To study the spread of the virus, measure “distance” by the number of home ranges separating a group of gorillas from the first group infected. Here are data on
What’s the line? You use the same bar of soap to shower each morning. The bar weighs 80 grams when it is new. Its weight goes down by 6 grams per day on the average. What is the equation of the regression line for predicting weight from days of use?
City mileage, highway mileage. We expect a car’s highway gas mileage to be related to its city gas mileage. Data for all 1198 vehicles in the government’s 2008 Fuel Economy Guide give the regression line highway mpg = 4.62 + (1.109 × city mpg)for predicting highway mileage from city
Changing the correlation. Use your calculator, software, or the Two Variable Statis-•••APPLET tical Calculator applet to demonstrate how outliers can affect correlation.
Changing the units. The healing rates plotted in Figure 4.6(c) are measured in micrometers (millionths of a meter) per hour. The correlation between healing rates for the two front limbs of newts is r = 0.358. If the measurements were made in inches per day, would the correlation change? Explain
Ebola and gorillas. The deadly Ebola virus is a threat to both people and gorillas in Central Africa. An outbreak in 2002 and 2003 killed 91 of the 95 gorillas in 7 home ranges in the Congo. To study the spread of the virus, measure “distance”by the number of home ranges separating a group of
Do heavier people burn more energy? The study of dieting described in Exercise 4.4 collected data on the lean body mass (in kilograms) and metabolic rate (in calories) for both female and male subjects:Sex F F F F F F F F F F Mass 36.1 54.6 48.5 42.0 50.6 42.0 40.3 33.1 42.4 34.5 Rate 995 1425 1396
Does fast driving waste fuel? How does the fuel consumption of a car change as its speed increases? Here are data for a British Ford Escort. Speed is measured in kilometers per hour, and fuel consumption is measured in liters of gasoline used per 100 kilometers traveled.4 Speed 10 20 30 40 50 60 70
Outsourcing by airlines. Does your plot for Exercise 4.5 show a positive association between maintenance outsourcing and delays caused by the airline? One airline is a high outlier in delay percent. Which airline is this? Aside from the outlier, does the plot show a roughly linear form? Is the
Do heavier people burn more energy? Describe the direction, form, and strength of the relationship between lean body mass and metabolic rate, as displayed in your plot for Exercise 4.4.
Outsourcing by airlines. Airlines have increasingly outsourced the maintenance of their planes to other companies. Critics say that the maintenance may be less carefully done, so that outsourcing creates a safety hazard. As evidence, they point to government data on percent of major maintenance
Do heavier people burn more energy? Metabolic rate, the rate at which the body consumes energy, is important in studies of weight gain, dieting, and exercise. We have data on the lean body mass and resting metabolic rate for 12 women who are subjects in a study of dieting. Lean body mass, given in
Beer and blood alcohol. Example 4.1 describes a study in which college students drank different amounts of beer. The response variable was their blood alcohol content(BAC). BAC for the same amount of beer might depend on other facts about the students. Name two other variables that could influence
Coral reefs. How sensitive to changes in water temperature are coral reefs? To find out, measure the growth of corals in aquariums where the water temperature is controlled at different levels. Growth is measured by weighing the coral before and after the experiment. What are the explanatory and
Explanatory and response variables? You have data on a large group of college students. Here are four pairs of variables measured on these students. For each pair, is it more reasonable to simply explore the relationship between the two variables or to view one of the variables as an explanatory
Fruit flies. The thorax lengths in a population of male fruit flies follow a Normal distribution with mean 0.800 millimeters (mm) and standard deviation 0.078 mm.What are the median and the first and third quartiles of thorax length?
Table A. Use Table A to find the value z of a standard Normal variable that satisfies each of the following conditions. (Use the value of z from Table A that comes closest to satisfying the condition.) In each case, sketch a standard Normal curve with your value of z marked on the axis.(a) The
Fruit flies. The common fruit fly Drosophila melanogaster is the most studied organism in genetic research because it is small, easy to grow, and reproduces rapidly. The length of the thorax (where the wings and legs attach) in a population of male fruit flies is approximately Normal with mean
Monsoon rains. The summer monsoon rains in India follow approximately a Normal distribution with mean 852 millimeters (mm) of rainfall and standard deviation 82 mm.(a) In the drought year 1987, 697 mm of rain fell. In what percent of all years will India have 697 mm or less of monsoon rain?(b)
Use the Normal table. Use Table A to find the proportion of observations from a standard Normal distribution that satisfies each of the following statements. In each case, sketch a standard Normal curve and shade the area under the curve that is the answer to the question.(a) z < 2.85 (b) z > 2.85
Men’s and women’s heights. The heights of women aged 20 to 29 are approximately Normal with mean 64 inches and standard deviation 2.7 inches. Men the same age have mean height 69.3 inches with standard deviation 2.8 inches. What are the z-scores for a woman 6 feet tall and a man 6 feet tall?
SAT versus ACT. In 2007, when she was a high school senior, Eleanor scored 680 on the mathematics part of the SAT. The distribution of SAT math scores in 2007 was Normal with mean 515 and standard deviation 114. Gerald took the ACT Assessment mathematics test and scored 27. ACT math scores for 2007
Monsoon rains. The summer monsoon brings 80% of India’s rainfall and is essential for the country’s agriculture. Records going back more than a century show that the amount of monsoon rainfall varies from year to year according to a distribution that is approximately Normal with mean 852
Running a mile. The times for the mile run of a large group of male college students are approximately Normal with mean 7.11 minutes and standard deviation 0.74 minutes. Use the 68–95–99.7 rule to answer the following questions. (Start by making a sketch like Figure 3.10.)(a) What range of
Running a mile. How fast can male college students run a mile? There’s lots of variation, of course. DuringWorldWar II, physical training was required for male students in many colleges, as preparation for military service. That provided an opportunity to collect data on physical performance on a
Mean and median. Figure 3.7 displays three density curves, each with three points marked on them. At which of these points on each curve do the mean and the median fall?
Mean and median. What is the mean μ of the density curve pictured in Figure 3.4?(That is, where would the curve balance?) What is the median? (That is, where is the point with area 0.5 on either side?)
Accidents on a bike path. Examining the location of accidents on a level, 3-mile bike path shows that they occur uniformly along the length of the path. Figure 3.4 displays the density curve that describes the distribution of accidents.(a) Explain why this curve satisfies the two requirements for a
Sketch density curves. Sketch density curves that describe distributions with the following shapes:(a) Symmetric, but with two peaks (that is, two strong clusters of observations)(b) Single peak and skewed to the left
Diplomatic scofflaws. Until Congress allowed some enforcement in 2002, the ST EP thousands of foreign diplomats in New York City could freely violate parking laws.Two economists looked at the number of unpaid parking tickets per diplomat over a five-year period ending when enforcement reduced the
Logging in the rain forest. “Conservationists have despaired over destruction of tropical rain forest by logging, clearing, and burning.” These words begin a report on S TE a statistical study of the effects of logging in Borneo. P 9 Charles Cannon of Duke University and his coworkers compared
Choose a summary. The shape of a distribution is a rough guide to whether the mean and standard deviation are a helpful summary of center and spread. For which of the following distributions would x and s be useful? In each case, give a reason for your decision.(a) Percents of foreign-born
x and s are not enough. The mean x and standard deviation s measure center and spread but are not a complete description of a distribution. Data sets with different shapes can have the same mean and standard deviation. To demonstrate this fact, use your calculator to find x and s for these two
x and s by hand. The air in poultry-processing plants often contains high concentrations of fungus spores, especially during the summer. To measure the presence of spores, air samples are pumped to an agar plate and “colony-forming units (CFUs)”are counted after an incubation period. The CFUs
Comparing investments. Should you put your money into a fund that buys stocks or a fund that invests in real estate? The answer changes from time to time, and unfortunately we can’t look into the future. Looking back into the past, the boxplots in Figure 2.2 compare the daily returns (in percent)
The Dallas Cowboys. The 2007 roster of the Dallas Cowboys professional football team included 9 defensive linemen and 10 offensive linemen. The weights in pounds of the defensive linemen were 300 300 295 255 298 298 300 310 300 and the weights of the offensive linemen were 312 305 340 320 366 324
Food oils. Table 1.4 (page 33) gives the ratio of two essential fatty acids in 30 food oils. Find the mean and the median for these data. Make a histogram of the data.What feature of the distribution explains why the mean is more than 10 times as large as the median?
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