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essential statistics

Essential Statistics 1st Edition David S Moore - Solutions

7.35 Sampling at a party. At a large block party there are 290 men and 110 women. You want to ask for opinions about how to improve the next party. To be sure that women's opin ions are adequately represented, you decide to choose a strati fied random sample (see the previous exercise) of 20 men
7.34 Stratified random samples. 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 are Bartington Hanover Norwood Park Riverside Berwyn Lemont
7.33 Sampling at a party. At a party there are 30 students ovet age 21 and 20 students under age 21. You choose at ran dom 3 of those over 21 and separately choose at tandom 2 of those uridet 21 to intetview about attitudes toward alcohol. You have given every student at the party the same chance
7.32 Seat belt use. A study in El Paso, Texas, looked at seat belt use by dtivers. 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,
7.31 Running red lights. The sample described in the previ ous exercise produced a list of 5024 licensed drivers. The in vestigators then chose an SRS of 880 of these drivers to answet questions about their driving habits.(a) How would you assign labels to the 5024 drivers? Use Ta ble B, starting
7.30 Nonresponse. Academic sample surveys, unlike com mercial polls, often discuss nonresponse. In a survey of drivers, researchers called a random sample of all listed residential tele phone numbers in the United States. Of 45,956 calls, 5029 were completed.'^ What was the rate of nonresponse for
7.29 Online polls. Example 7.3 reports an online poll in which 97% of the respondents opposed issuing driver's licenses to illegal immigrants. National random samples taken at the same time showed about 70% of the respondents opposed to such licenses. Explain briefly to someone who knows no
7.28 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
7.27 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 Os 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,
7.26 Random digits. In usirrg Table B repeatedly to choose random samples, you should not always begin at the same place, such as line 101. Why ru)t?
7.25 Sampling pharmacists. All pharmacists in the Cana dian 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
7.24 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.(a) How would you label the plots?(b) Choose the first 5 plots
7.23 Sampling telephone area codes. There are approxi mately 341 active telephone area codes covering Canada, the United States, and some Caribbean areas. (More are created regularly.) Choose an SRS of 25 ot these area codes for a study of available telephone numbers. (If you use Table B rather
7.22 Do you trust the Internet? You want to ask a sample of college students the question "How much do you trust in formation 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
7.21 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
7.20 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 na tional adults, aged 18 and older, conducted Dec. 6-9,
7.19 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 phoiaes, and another 25% have unlisted telephone numbers. The sam ple will certainly suffer from(a) nonresponse.(h)
7.18 You want to choose an SRS of 5 of the 7200 salaried em ployees 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)
7.17 You are using the table of random digits to choose a simple random sample of 6 students from a class of 30 stu dents. 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) 04,
7.16 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
7.15 The Web 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.
7.14 A committee on community relations in a college town plans to survey local businesses about the importance of stu dents as customers. From telephone book listings, the com mittee chooses 150 businesses at random. Of these, 73 return the questionnaire mailed by the committee. The population for
7.13 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 1161
7.12 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
7.11 Ring-no-answer. A common form of nonresponse in telephone surveys is "ring-noanswer."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 house holds in Italy during the periods January 1 to
7.10 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 pop ulation. In South Korea, random samples by
7.9 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?
7.8 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
7.7 Minority managers. A firm wants to understand the attitudes of its minority managers toward its system for assessing maiaagement performance. Below is a list of all the firm's managers who are members of minority groups. Use software or Table B at line 139 to choose six to he interviewed in
7.6 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 resi dents. Use software or Table B to select a simple random sample of three of the following apartment complexes. If you use
7.5 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
7.4 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 collect ing student opinions for a class assignment. Explain why this sampling method is almost certainly biased.
7.3 Customer satisfaction. A department store mails a customer satisfaction survey to peo ple 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
7.2 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
7.1 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
6.45 Canadian students gambling. Here are the percents of students at four universities in Ontario who engage in several types of gambling:^'^(LOTTO 6/49 is a nationwide Canadian lottery. Pro-Line is a sports betting game offered by the Ontario provincial govern ment.) Make a graph that compares
6.44 Influence: monkey calls. Table 6.1 contains data on the response of 37 monkey neurons to pure tones and to mon key calls. You made a scatterplot of these data in Exercise 6.25.(a) Find the least-squares line for predicting a neuron's call respoiase from its pure tone response. Add the line to
6.43 Influence: hot mutual funds? Investment advertise ments always warn that "past performance does not guaran tee future results." Here is an example that shows why you should pay attention to this warning. Stocks fell sharply in 2002, then rose sharply in 2003. The table below gives the percent
6.42 Casting aluminum. In casting metal parts, molten fci'metal flows through a "gate" into a die that shapes the part.The gate velocity (the speed at which metal is forced through the gate) plays a critical role in die casting. A firm that casts cylindrical aluminum pistons examined 12 types
6.41 Change in the Serengeti. Long-term records from the■■-.Serengeti National Park in Tanzania show interesting ecolog ical relationships. When wildebeest are more abundant, they graze the grass more heavily, so there are fewer fires and more trees grow. Lions feed more successfully when there
6.40 Prey attract predators. Here is one way in which kii nature regulates the size of animal populations: high popu lation density attracts predators, who remove a higher propor tion of the population than when the density of the prey is low.One study looked at kelp perch and their common
6.39 A big toe problem. Hallux abducto valgus (call it ■L HAV) is^a deformation of the big toe that is not common in youth and often requires surgery. Doctors used X-rays to mea sure the angle (in degrees) of deformity in 38 consecutive pa tients under the age of 21 who came to a medical center
6.38 Cicadas as fertilizer? Periodically, swarms of ci-■if cadas emerge from the ground in the eastern United States, live for about six weeks, then die. There are so many cicadas that their dead bodies can serve as fertilizer and increase plant growth. In an experiment, a researcher added 10
6.37 Big government? The data file ex06-37.dat on the text CD and Web site contains the percent of gross domestic prod uct (GDP, the total value of all goods and services a country produces) taken by the government in 82 countries. For exam ple, the government share of GDP is 12.28% in Canada and
6.36 More on global warming. Side-by-side boxplots offer a different look at the data. Group the data into periods of roughly equal length: 1917 to 1939, 1940 to 1962, 1963 to 1985, and 1986 to 2008. Make boxplots to compare ice breakup dates in these four time periods. Write a brief description of
6.35 Global warming? Because of the high stakes, the falling of the tripod has been carefully observed for many years. If the date the tripod falls has been getting earlier, that may be evi dence for the effects of global warming.(a) Make a time plot of the date the tripod falls against year.(b)
6.34 When does the ice break up? We have 92 years of data on the date of ice breakup on the Tanana River. Describe the distribution of the breakup date with both a graph or graphs and appropriate numerical summaries. What is the median date (month and day) for ice breakup?
6.33 More on the Mississippi River. The data in Table 6.2 are a time series. Make a time plot that shows how the volume of water in the Mississippi changed between 1954 and 2001.What does the time plot reveal that the histogram from the previous exeifcise does not? It is a good idea to always make
6.32 The Mississippi River. Table 6.2 gives the volume of water discharged by the Mississippi River into the Gulf of Mex ico for each year from 1954 to 2001.'" The units are cubic kilo meters of water.(a) Make a graph of the distribution of water volume. Describe the overall shape of the
6.31 Weeds among the corn, continued. We can also use regression to analyze the data on weeds and corn yield. The ad vantage of regression over the side-by-side comparison in the previous exerqise is that we can use the fitted line to draw con clusions for counts of weeds othet than the ones the
6.30 Weeds among the corn. Lamb's-quarter is a common weed that interferes with the growth of corn. An agriculture researcher planted corn at the same rate in 16 small plots of ground, then weeded the plots by hand to allow a fixed number of lamb's-quarter plants to grow in each meter of corn row.
6.29 Interpreting correlation. The same article that claims that the cotrelation between changes in stock prices in Eu rope and the United States is 0.8 goes on to say: "Crudely, that means that movements on Wall Street can explain 80% of price movements in Europe." Is this true? What is the
6.28 Moving in step? One reason to invest abroad is that markets in different countries don't move in step. When Amer ican stocks go down, foreign stocks may go up. So an investor who holds both bears less risk. That's the theory. Now we read: "The correlation between changes in American and Eu
6.27 Statistics for investing. Joe's retirement plan invests in stocks through an "index fund" that follows the behavior of the Stock market as a whole, as measured by the S&.P 500 stock in dex. Joe wants to buy a mutual fund that does not track the index closely. He reads that monthly returns from
6.26 Remember what you ate. How well do people remem ber their past diet? Data are available for 91 people who were asked about their diet when they were 18 years old. Researchers asked them at about age 55 to describe their eating habits at age 18. For each subject, the researchers calculated the
6.25 Monkey calls. The usual way to study the brain's re sponse to souiads is to have subjects listen to "pure tones."The respoiase to recognizable sounds may differ. To compare re sponses, researchers anesthetized macaque monkeys. They fed pure tones and also monkey calls directly to their brains
6.24 The end of smoking, continued. Use your regression line from Exercise 6.22 to predict the percent of adults who will smoke in 2050. Why is your result impossible? Why was it foolish to use the regression line for this prediction?
6.23 Squirrels and their food supply. Animal species pro duce more offspring when their supply of food goes up. Some animals appear able to anticipate unusual food abundance. Red squirrels eat seeds from pine cones, a food source that occa sionally has very large crops. Here are data on art index
6.24 The end of smoking, continued. Use your regression line from Exercise 6.22 to predict the percent of adults who will smoke in 2050. Why is your result impossible? Why was it foolish to use the regression line for this prediction?(b) Accordmg to your regression line, how much did smoking
6.23 Squirrels and their food supply. Animal species pro duce more offspring when their supply of food goes up. Some animals appear able to anticipate unusual food abundance. Red squirrels eat seeds from pine cones, a food source that occa sionally has very large crops. Here are data on art index
6.22 The end of smoking? The number of adult Americans who smoke continues to drop. Here are estimates of the percent of adults (aged 18 and over) who were smokers in the years be tween 1965 and 2006:'°Year Smokers Year Smokers 1965 41.9 1993 24.8 1974 37.0 1997 24.6 1979 33.3 2000 23.1 1983 31.9
6.21 Thin monkeys, fat monkeys. Animals and people that take in more energy than they expend will get fatter. Here are data on 12 rhesus monkeys; 6 lean monkeys (4% to 9% body fat) and 6 obese monkeys (13% to 44% body fat). The data re port the energy expended in 24 hours (kilojoules per minute)and
6.20 Growing icicles. Table 4.2 (page 87) gives data on the growth of icicles over time. Let's look again at Run 8903, for which a slower flow of water produces faster growth.(a) How can you tell from a calculation, without drawing a scatterplot, that the pattern of growth is very close to a
6.19 Prediction? Use the regression equation in the previous exercise to predict the weight of the soap after 30 days. Why is it clear that your answer makes no sense? What's wrong with using the regression line to predict weight after 30 days?
6.18 Regression. Find the equation of the least-squares re gression line for predicting soap weight from day.(a) What is the equation? Explain what it tells us about the rate at which the soap lost weight.(b) Mr. Boggs did not measure the weight of the soap on Day 4-Use the regression equation to
6.17 Scatterplot and correlation. Plot the weight of the bar of soap against day. Is the overall pattern roughly linear? Based on your scatterplot, is the correlation between day and weight close to 1, positive but not close to 1, close to 0, negative but not close to — 1, or close to — 1 ?
6.16 Breaking bolts. Mechanical measurements on suppos edly identical objects usually vary. The variation often follows a Normal distribution. The stress required to break a type of bolt varies Normally with mean 75 kilopounds per square inch(ksi) and standard deviation 8.3 ksi.(a) What percent of
6.15 The Medical College Admission Test. Almost all medical schools in the United States and Canada require ap plicants to take the Medical College Admission Test (MCAT).The scores of applicants on the biological sciences part of the MCAT in 2007 were approximately Normal with mean 9.6 and standard
6.14 Body mass index. Your body mass index (BMl) is your weight in kilograms divided by the square of your height in meters. Online BMI calculators allow you to enter weight in pounds and height in inches. High BMI is a commoir but con troversial indicator of overweight or obesity. A study by the
6.13 Pine needles. The lengths of needles ftom Aleppo pines follow approximately the Normal distribution with mean 9.6 centimeters (cm) and standard deviation 1.6 cm. According to the 68-95—99.7 rule, what range of lengths covers the center 95% of Aleppo pine needles? What perceirt of needles are
6.12 Weights aren't Normal. The heights of people of the same sex and similar ages follow a Normal distribution reason ably closely. Weights, on the other hand, are not Normally dis tributed. The weights of women aged 20 to 29 have mean 141.7 pounds and median 133.2 pounds. The first and third
6.11 Distribution shapes. Biologists commonly act as if measurements on many individuals from the same species fol low a Normal distribution. They therefore use the mean T and standard deviation s as numerical summaries.(a) Make stemplots of the lengths of needles of Aleppo pines and of Torrey
6.10 Genetic engineering for cancer treatment. Here's a new idea for treating advanced melanoma, the most serious kind of skin cancer. Genetically engineer white blood cells to better recognize and destroy cancer cells, then infuse these cells into patients. The subjects in a small initial study
6.9 Two species of pine trees. The Aleppo pine and the Torrey pine are widely planted as ornamental trees in Southem California. Here are the lengths (centimeters) of 15 Aleppo pine needles:^10.2 7.2 7.6 9.3 12.1 10.9 9.4 11.3 8.5 8.5 12.8 8.7 9.0 9.0 9.4 Here are the lengths of 18 needles from
6.8 Nitrogen in diamonds. Scientists made detailed chemi cal analyses of 24 of the diamonds from Exercise 6.5. The abun dances of various elements give clues to how the diamonds were formed. Here are the data on nitrogen content, in parts per mil lion:487 1430 60 244 196 274 41 54 473 30 98 41 273
6.7 Recycling. Of the municipal solid waste described in the previous exercise, about 55% is discarded, 32.5% is recovered through recycling or composting, and 12.5% is hurried to pro duce energy. Here are the percents of several materials in solid waste that are! recycled:Material Aluminum cans
6.6 Garbage. The formal name for garbage is "municipal solid waste." Here is a breakdown of the materials that make up American municipal solid waste, in millions of tons:''Material Weight Food 31.3 Glass 13.2 Metals 19.1 Paper, paperboard 85.3 Plastics 29.5 Rubber, leather, textiles 18.3 Wood 13.9
6.5 How heavy are diamonds? Here are the weights (in milligrams) of 58 diamonds from a nodule carried up to the earth's surface in surrounding rock. This represents a single population of diamonds formed in a single event deep in the earth.'Make a graph that shows the distribution of weights of dia
6.4 The state of the country. The Pew Research Center re ports the following percents of American adults who said "sat isfied" when asked, "All in all, are you satisfied or dissatisfied with the way things are going in this country today ?"^Year Percent Year Percent Year Percent 1988 55 1996 29
6.3 What do you think of Microsoft? The Pew Reseatch Center asked a raridom sample of adults whether they had fa vorable or unfavorable opinions of a number of major compa nies. Answers to such questions depend a lot on recent news.Here are the percents with favorable opinions for several of the
6.2 Data on mice. For a biology project, you measure the tail length in centimeters and weight in grams of 12 mice of the same variety. What units of rneasurement do each of the fol lowing have?(a) The mean length of the tails.(h) The fitst quartile of the tail lengths.(c) The standard deviation of
6.1 Describing colleges. Popular magazines rank colleges and universities on their academic quality in serving under graduate students. Below are several variables that might con tribute to ranking colleges. Which of these are categorical and which are quantitative?(a) Percent of freshmen who
5.47 Effects of health care spending. Table 1.3 (page■ill 19) gives United Nations data on annual health care spending per person in 38 richer nations. The United States, at$5711 per person, is a high outlier. The data file 6x05-47.dat on the text CD and Web site adds more information about these
5.46 Saving energy with solar panels. Exercise 4.35 (page IfeiSS) gives monthly data on outside temperature (in degree-days per day) and natural gas consumed for a house in the Mid west both before and after installing solar panels. A cold win ter month in this location may average 45 degree-days
5.45 Climate change. Global warming has many indi-Hli rect effects on climate. For example, the summer monsoon winds in the| Arabian Sea bring rain to India and are critical for agriculture. As the climate warms and winter snow cover in the vast landmass of Europe and Asia decreases, the land
5.44 Predicting tropical storms. William Gray heads k» the Tropical Meteorology Project at Colorado State Uni versity. His forecasts before each year's hurricane season at tract lots of attention. Here are data on the number of named Atlantic tropical storms predicted by Dr. Gray and the actual
5.43 A computer game. A multimedia statistics learn-Hiiti ing system includes a test of skill in using the computet's mouse. The software displays a circle at a random location on the computer ^screen. The subject clicks in the circle with the mouse as quickly as possible. A new citcle appears as
5.42 Beavers and beetles. Do beavers benefit beetles? Re-'searchers laid out 23 circular plots, each 4 meters in diameter, in an area where beavers were cutting down cottonwood trees.In each plot, they counted the number of stumps from trees cut by beavers and the number of clusters of beetle
5.41 Regression to the mean. Figure 4.6 (page 85) displays the relationship between golfers' scores on the first and sec ond tounds of the 2007 Masters Tournament. The least-squares line for predicting second-round scores from first-round scores has equation y = 61.93+0.180x. Find the predicted
5.40 Some regression math. Use the equation of the leastsquates regression line (box on page 94) to show that the re gression line for predicting y from x always passes through the point {x,y). That is, when x=x, the equation gives y = y-
5.39 Learning online. Many colleges offer online versions of courses that are also taught in the classroom. It often happens
5.38 Do artificial sweeteners cause weight gain? People who use artificial sweeteners in place of sugar tend to be heavier than people who use sugar. Does this mean that artificial sweet eners cause weight gain? Give a more plausible explanation for this association.
5.37 Managing diabetes, continued. Add three regression lines for predicting FPG from HbA to your scatterplot from Ex ercise 5.35: for all 18 subjects, for all except Subject 15, and for all except Subject 18. Is either Subject 15 or Subject 18 strongly influential for the least-squares line?
5.39 Learning online. Many colleges offer online versions of courses that are also taught in the classroom. It often happens limeters. Use the fact that there are 100 centimeters in a meter to show that the two predictions are the same (up to roundoff error).
5.38 Do artificial sweeteners cause weight gain? People who use artificial sweeteners in place of sugar tend to be heavier than people who use sugar. Does this mean that artificial sweet eners cause weight gain? Give a more plausible explanation for this association.
5.37 Managing diabetes, continued. Add three regression lines for predicting FPG from HbA to your scatterplot from Ex ercise 5.35: for all 18 subjects, for all except Subject 15, and for all except Subject 18. Is either Subject 15 or Subject 18 strongly influential for the least-squares line?
5.36 The effect of changing units. The equation of a re gression line, unlike the correlation, depends on the units we use to measure the explanatoty and response variables. Hereare data on knee height and overall height (in centimeters) for five elderly men:Knee height x Height y 57.7 192.1 47.4
5.35 Managing diabetes. People with diabetes measute theit fasting plasma glucose (FPG) after fasting for at least 8 hours. Another measurement, made at regular medical check ups, is called HbA. This is roughly the percent of red blood cells that have a glucose molecule attached. It measures
5.34 Always plot your data! Table 5.1 presents fout sets of data prepared by the statistician Ftank Anscombe to illustrate the dangers of calculating without fitst plotting the data.''(a) Without I making scatterplots, find the correlation and the least-squates regression line for all four data
5.33 Keeping water clean. Keeping watet supplies clean re quires regulat measurement of levels of pollutants. The mea surements are indirect—a typical analysis involves forming a dye by a chemical reaction with the dissolved pollutant, then passing light through the solution and measuring

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