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essentials of statistics
The Basic Practice Of Statistics 5th Edition David S Moore - Solutions
Do angry people have more heart disease? People who get angry easily tend ST EP to have more heart disease. That’s the conclusion of a study that followed a random sample of 12,986 people from three locations for about four years. All subjects were free of heart disease at the beginning of the
The Mediterranean diet. Cancer of the colon and rectum is less common in the Mediterranean region than in otherWestern countries. The Mediterranean diet contains little animal fat and lots of olive oil. Italian researchers compared 1953 patients with colon or rectal cancer with a control group of
College degrees. “Colleges and universities across the country are grappling with S TE Pthe case of the mysteriously vanishing male.” So said an article in the Washington Post. Here are data on the numbers of degrees earned in 2009–2010, as projected by the National Center for Education
Animal testing. “It is right to use animals for medical testing if it might save human ST EP lives.”The General Social Survey asked 1152 adults to react to this statement. Here is the two-way table of their responses:Response Male Female Strongly agree 76 59 Agree 270 247 Neither agree nor
Life at work. The University of Chicago’s General Social Survey asked a repre-T EP sentative sample of adults this question: “Which of the following statements best describes how your daily work is organized? 1: I am free to decide how my daily work is organized. 2: I can decide how my daily
Obesity and health. To estimate the health risks of obesity, we might compare how long obese and nonobese people live. Smoking is a lurking variable that may reduce the gap between the two groups, because smoking tends to both reduce weight and lead to earlier death. So if we ignore smoking, we may
Discrimination?Wabash Tech has two professional schools, business and law. Here are two-way tables of applicants to both schools, categorized by gender and admission decision. (Although these data are made up, similar situations occur in reality.)10 Business Admit Deny Male 480 120 Female 180 20
Association is not causation. The data in Table 6.2 show that single men are more likely to hold lower-grade jobs than are married men. We should not conclude that single men can help their career by getting married. What lurking variables might help explain the association between marital status
Marital status and job grade. One way to see the relationship is to look at who holds Grade 1 jobs.(a) There are 874 married men with Grade 1 jobs, and only 58 single men with such jobs. Explain why these counts by themselves don’t describe the relationship between marital status and job
Conditional distribution. Give (in percents) the conditional distribution of job grade among single men. Should your percents add to 100% (up to roundoff error)?
Percents. What percent of single men hold Grade 1 jobs? What percent of Grade 1 jobs are held by single men?
Marginal distributions. Give (in percents) the two marginal distributions, for marital status and for job grade. Do each of your two sets of percents add to exactly 100%?If not, why not?
Helping cocaine addicts.Will giving cocaine addicts an antidepressant drug help them break their addiction? An experiment assigned 24 chronic cocaine users to take the antidepressant drug desipramine, another 24 to take lithium, and another 24 to take a placebo. (Lithium is a standard drug to treat
Graduate school for men and women. The College of Liberal Arts at a large university looks at its graduate students classified by their sex and field of study. Here are the data:7 Female Male English 136 89 Foreign languages 61 25 History 35 55 Philosophy 10 54 Political science 29 35 Find the two
A college looks at the grade point average (GPA) of its full-time and part-time students.Grades in science courses are generally lower than grades in other courses.There are few science majors among part-time students but many science majors among full-time students. The college finds that
A bar graph showing the conditional distribution of opinion among female respondents would have(a) 2 bars. (b) 5 bars. (c) 10 bars.
Your percent from the previous exercise is part of(a) the marginal distribution of opinion about marriage.(b) the conditional distribution of sex among those who thought they were almost certain to be married.(c) the conditional distribution of opinion about marriage among women.
What percent of those who thought they were almost certain to be married were female?(a) about 40% (b) about 45% (c) about 61%
Your percent from the previous exercise is part of(a) the marginal distribution of opinion about marriage.(b) the conditional distribution of sex among those who thought they were almost certain to be married.(c) the conditional distribution of opinion about marriage among women.
What percent of females thought that they were almost certain to be married in the next 10 years?(a) about 40% (b) about 45% (c) about 61%
Your percent from the previous exercise is part of(a) the marginal distribution of sex.(b) the marginal distribution of opinion about marriage.(c) the conditional distribution of sex among adolescents with a given opinion.Comstock Images/Age fotostock
The percent of females among the respondents was(a) about 46%. (b) about 54%. (c) about 86%.
Effects of health care spending. Table 1.3 (page 22) 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 ex05–56.dat on the text CD and Web site adds more information about these
Saving energy with solar panels. Exercise 4.43 (page 121) gives monthly data on outside temperature (in degree-days per day) and natural gas consumed for a house in the Midwest both before and after installing solar panels.Acold winter month in this location may average 45 degree-days per day
Climate change. Global warming has many indirect 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 heats more
Predicting tropical storms.William Gray heads the Tropical Meteorology Project at Colorado State University (well away from the hurricane belt). His forecasts before each year’s hurricane season attract lots of attention. Here are data on the number of named Atlantic tropical storms predicted by
A computer game. A multimedia statistics learning system includes a test of skill in using the computer’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 circle appears as soon as the
Beavers and beetles. Do beavers benefit beetles? Researchers 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 larvae.
Guessing a regression line. In the Correlation and Regression applet, click on the APPLET •••scatterplot to create a group of 15 to 20 points from lower left to upper right with a clear positive straight-line pattern (correlation around 0.7). Click the “Draw line”button and use the mouse
Is regression useful? In Exercise 4.41 (page 121) you used the Correlation and Re- APPLET •••gression applet to create three scatterplots having correlation about r = 0.7 between the horizontal variable x and the vertical variable y. Create three similar scatterplots again, and click the
Regression to the mean. We expect that students who do well on the midterm exam in a course will usually also do well on the final exam. Gary Smith of Pomona College looked at the exam scores of all 346 students who took his statistics class over a 10-year period.17 The least-squares line for
Regression to the mean. Figure 4.8 (page 114) displays the relationship between golfers’ scores on the first and second rounds of the 2007 Masters Tournament. The least-squares line for predicting second-round scores from first-round scores has equationˆy = 61.93 + 0.180x. Find the predicted
Some regression math. Use the equation of the least-squares regression line (box on page 130) to show that the regression line for predicting y from x always passes through the point (x, y). That is, when x = x, the equation gives ˆy = y.
Workers’ incomes. Here is another example of the group effect cautioned about in the previous exercise. Explain how, as a nation’s population grows older, median income can go down for workers in each age group, yet still go up for all workers.
Grade inflation and the SAT. The effect of a lurking variable can be surprising when individuals are divided into groups. In recent years, the mean SAT score of all high school seniors has increased. But the mean SAT score has decreased for students at each level of high school grades (A, B, C, and
Learning online. Many colleges offer online versions of courses that are also taught in the classroom. It often happens that the students who enroll in the online version do better than the classroom students on the course exams. This does not show that online instruction is more effective than
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 sweeteners cause weight gain? Give a more plausible explanation for this association.
Managing diabetes, continued. Add three regression lines for predicting FPG from HbA to your scatterplot from Exercise 5.39: 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? Explain in
The effect of changing units. The equation of a regression line, unlike the correlation, depends on the units we use to measure the explanatory and response variables.Here are data on knee height and overall height (in centimeters) for five elderly men:Knee height x 57.7 47.4 43.5 44.8 55.2 Height
Managing diabetes. People with diabetes must manage their blood sugar levels carefully. They measure their fasting plasma glucose (FPG) several times a day with a glucose meter. Another measurement, made at regular medical checkups, is called HbA. This is roughly the percent of red blood cells that
Always plot your data! Table 5.1 presents four sets of data prepared by the statistician Frank Anscombe to illustrate the dangers of calculating without first plotting the data.15(a) Without making scatterplots, find the correlation and the least-squares regression line for all four data sets. What
Our brains don’t like losses. Exercise 4.29 (page 116) describes an experiment that showed a linear relationship between how sensitive people are to monetary losses (“behavioral loss aversion”) and activity in one part of their brains (“neural loss aversion”).(a) Make a scatterplot with
Sparrowhawk colonies. One of nature’s patterns connects the percent of adult birds in a colony that return from the previous year and the number of new adults that join the colony. Here are data for 13 colonies of sparrowhawks:14 Percent return x 74 66 81 52 73 62 52 45 62 46 60 46 38 New adults
Keeping water clean. Keeping water supplies clean requires regular measurement of levels of pollutants. The measurements 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 its
Sisters and brothers. How strongly do physical characteristics of sisters and brothers correlate? Here are data on the heights (in inches) of 11 adult pairs:12 Brother 71 68 66 67 70 71 70 73 72 65 66 Sister 69 64 65 63 65 62 65 64 66 59 62(a) Use your calculator or software to find the correlation
Going to class. A study of class attendance and grades among first-year students at a state university showed that in general students who attended a higher percent of their classes earned higher grades. Class attendance explained 16% of the variation in grade index among the students. What is the
What’s my grade? In Professor Friedman’s economics course the correlation between the students’ total scores prior to the final examination and their finalexamination scores is r = 0.6. The pre-exam totals for all students in the course have mean 280 and standard deviation 30. The final-exam
Husbands and wives. The mean height of American women in their twenties is about 64 inches, and the standard deviation is about 2.7 inches. The mean height of men the same age is about 69.3 inches, with standard deviation about 2.8 inches.Suppose that the correlation between the heights of husbands
Merlins breeding. Exercise 4.44 (page 122) gives data on the number of breeding pairs of merlins in an isolated area in each of nine years and the percent of males who returned the next year. The data show that the percent returning is lower after successful breeding seasons and that the
Does social rejection hurt? Exercise 4.45 (page 122) gives data from a study that shows that social exclusion causes “real pain.”That is, activity in an area of the brain that responds to physical pain goes up as distress from social exclusion goes up. A scatterplot shows a moderately strong
Measuring water quality. Biochemical oxygen demand (BOD) measures organic pollutants in water by measuring the amount of oxygen consumed by microorganisms that break down these compounds. BOD is hard to measure accurately. Total organic carbon (TOC) is easy to measure, so it is common to measure
Penguins diving. A study of king penguins looked for a relationship between how deep the penguins dive to seek food and how long they stay underwater.10 For all but the shallowest dives, there is a linear relationship that is different for different penguins. The study report gives a scatterplot
Because elderly people may have difficulty standing to have their heights measured, a study looked at predicting overall height from height to the knee. Here are data(in centimeters) for five elderly men:Knee height x 57.7 47.4 43.5 44.8 55.2 Height y 192.1 153.3 146.4 162.7 169.1 Use your
In addition to the regression line in Exercise 5.22, the report on the Mumbai measurements says that r 2 = 0.95. This suggests that(a) although armspan and height are correlated, armspan does not predict height very accurately.(b) height increases by0.95 = 0.97 cm for each additional centimeter of
By looking at the equation of the least-squares regression line in Exercise 5.22, you can see that the correlation between height and armspan is(a) greater than zero.(b) less than zero.(c) Can’t tell without seeing the data.
According to the regression line in Exercise 5.22, the predicted height of a child with armspan 100 cm is about(a) 106.4 cm. (b) 99.4 cm. (c) 93 cm.
Measurements on young children in Mumbai, India, found this least-squares line for predicting height y from armspan x:9ˆy = 6.4 + 0.93x All measurements are in centimeters (cm). How much on the average does height increase for each additional centimeter of armspan?(a) 0.93 cm (b) 6.4 cm (c) 7.33 cm
Smokers don’t live as long (on the average) as nonsmokers, and heavy smokers don’t live as long as light smokers. You regress the age at death of a group of male smokers on the number of packs per day they smoked. The slope of your regression line(a) will be greater than 0.(b) will be less than
Fred keeps his savings in his mattress. He began with $500 from his mother and adds$100 each year. His total savings y after x years are given by the equation(a) y = 500 + 100x. (b) y = 100 + 500x. (c) y = 500 + x.
The points on a scatterplot lie close to the line whose equation is y = 4 − 3x. The slope of this line is(a) 4. (b) 3. (c) −3.
The slope of the line in Figure 5.9 is closest to(a) −1. (b) 0. (c) 1.
Figure 5.9 is a scatterplot of reading test scores against IQ test scores for 14 fifthgrade children. The line is the least-squares regression line for predicting reading score from IQ score. If another child in this class has IQ score 110, you predict the reading score to be close to(a) 50. (b)
Bushmeat. African peoples often eat “bushmeat,” the meat of wild animals. Bush-S TE Pmeat is widely traded in Africa, but its consumption threatens the survival of some animals in the wild. Bushmeat is often not the first choice of consumers—they eat bushmeat when other sources of protein are
Does social rejection hurt? We often describe our emotional reaction to social ST EP rejection as “pain.” Does social rejection cause activity in areas of the brain that are known to be activated by physical pain? If it does, we really do experience social and physical pain in similar ways.
Merlins breeding. Often the percent of an animal species in the wild that survive ST EP to breed again is lower following a successful breeding season. This is part of nature’s self-regulation to keep population size stable. A study of merlins (small falcons) in northern Sweden observed the
Saving energy with solar panels. We have data from a house in the Midwest ST EP that uses natural gas for heating. Will installing solar panels reduce the amount of gas consumed? Gas consumption is higher in cold weather, so the relationship between outside temperature and gas consumption is
Brighter sunlight? The brightness of sunlight at the earth’s surface changes over ST EP time depending on whether the earth’s atmosphere is more or less clear. Sunlight dimmed between 1960 and 1990. After 1990, air pollution dropped in industrial countries. Did sunlight brighten? Here are data
Match the correlation. You are going to use the Correlation and Regression applet APPLET ••• to make scatterplots with 10 points that have correlation close to 0.7. The lesson is that many patterns can have the same correlation. Always plot your data before you trust a correlation.(a) Click
Correlation is not resistant. Go to the Correlation and Regression applet. Click on the scatterplot 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).(a) Add one point at the upper right that is in line with the
Sloppy writing about correlation. Each of the following statements contains a blunder. Explain in each case what is wrong.(a) “There is a high correlation between the gender of American workers and their income.”(b) “We found a high correlation (r = 1.09) between students’ ratings of
Teaching and research. A college newspaper interviews a psychologist about student ratings of the teaching of faculty members. The psychologist says, “The evidence indicates that the correlation between the research productivity and teaching rating of faculty members is close to zero.” The
Statistics for investing. A mutual funds company’s newsletter says, “A welldiversified portfolio includes assets with low correlations.” The newsletter includes a table of correlations between the returns on various classes of investments. For example, the correlation between municipal bonds
Statistics for investing. Investment reports now often include correlations. Following a table of correlations among mutual funds, a report adds: “Two funds can have perfect correlation, yet different levels of risk. For example, Fund A and Fund B may be perfectly correlated, yet FundAmoves 20%
The effect of changing units. Changing the units of measurement can dramatically alter the appearance of a scatterplot. Return to the data on knee height and overall height in Exercise 4.23:Knee height x 57.7 47.4 43.5 44.8 55.2 Height y 192.1 153.3 146.4 162.7 169.1 Both heights are measured in
Thinking about correlation. Exercise 4.26 presents data on the heights of women and of the men they date.(a) If heights were measured in centimeters rather than inches, how would the correlation change? (There are 2.54 centimeters in an inch.)(b) How would r change if all the men were 6 inches
Attracting beetles. To detect the presence of harmful insects in farm fields, we can put up boards covered with a sticky material and examine the insects trapped on the boards. Which colors attract insects best? Experimenters placed six boards of each of four colors at random locations in a field
How many corn plants are too many? How much corn per acre should a farmer plant to obtain the highest yield? Too few plants will give a low yield. On the other hand, if there are too many plants, they will compete with each other for moisture and nutrients, and yields will fall. To find the best
How fast do icicles grow? Japanese researchers measured the growth of icicles in a cold chamber under various conditions of temperature, wind, and water flow.14 Table 4.2 contains data produced under two sets of conditions. In both cases, there was no wind and the temperature was set at −11◦C.
Sulfur, the ocean, and the sun. Sulfur in the atmosphere affects climate by influencing formation of clouds. The main natural source of sulfur is dimethylsulfide(DMS) produced by small organisms in the upper layers of the oceans. DMS production is in turn influenced by the amount of energy the
Our brains don’t like losses. Most people dislike losses more than they like gains.In money terms, people are about as sensitive to a loss of $10 as to a gain of $20. To discover what parts of the brain are active in decisions about gain and loss, psychologists presented subjects with a series of
Sparrowhawk colonies. One of nature’s patterns connects the percent of adult birds in a colony that return from the previous year and the number of new adults that join the colony. Here are data for 13 colonies of sparrowhawks:11 Percent return 74 66 81 52 73 62 52 45 62 46 60 46 38 New adults 5
Coffee and deforestation. Coffee is a leading export from several developing countries.When coffee prices are high, farmers often clear forest to plant more coffee trees. Here are five years of data on prices paid to coffee growers in Indonesia and the percent of forest area lost in a national park
Data on dating. A student wonders if tall women tend to date taller men than do short women. She measures herself, her dormitory roommate, and the women in the adjoining rooms; then she measures the next man each woman dates. Here are the data (heights in inches):Women (x) 66 64 66 65 70 65 Men (y)
Can children estimate their own reading ability? To study this question, investigators asked 60 fifth-grade children to estimate their own reading ability, on a scale from 1 (low) to 5 (high). Figure 4.9 is a scatterplot of the children’s estimates (response)against their scores on a reading test
Scores at the Masters. The Masters is one of the four major golf tournaments.Figure 4.8 is a scatterplot of the scores for the first two rounds of the 2007 Masters for all of the golfers entered. Only the 60 golfers with the lowest two-round total advance to the final two rounds. The plot has a
Because elderly people may have difficulty standing to have their heights measured, a study looked at predicting overall height from height to the knee. Here are data(in centimeters) for five elderly men:Knee height x 57.7 47.4 43.5 44.8 55.2 Height y 192.1 153.3 146.4 162.7 169.1 Use your
For a biology project, you measure the weight in grams and the tail length in millimeters of a group of mice. The correlation is r = 0.7. If you had measured tail length in centimeters instead of millimeters, what would be the correlation? (There are 10 millimeters in a centimeter.)(a) 0.7/10 =
If women always married men who were 2 years older than themselves, the correlation between the ages of husband and wife would be(a) 1. (b) 0.5. (c) Can’t tell without seeing the data.
The points on a scatterplot lie very close to the line whose equation is y = 4 − 3x.The correlation between x and y is close to(a) −3. (b) −1. (c) 1.
If the correlation between two variables is close to 0, you can conclude that a scatterplot would show(a) a strong straight-line pattern.(b) a cloud of points with no visible pattern.(c) no straight-line pattern, but there might be a strong pattern of another form.
What are all the values that a correlation r can possibly take?(a) r ≥ 0 (b) 0 ≤ r ≤ 1 (c) −1 ≤ r ≤ 1
If we leave out the low outlier, the correlation for the remaining 13 points in Figure 4.7 is closest to(a) 0.5. (b) −0.5. (c) 0.95.
Figure 4.7 is a scatterplot of reading test scores against IQ test scores for 14 fifthgrade children. There is one low outlier in the plot. The IQ and reading scores for this child are(a) IQ = 10, reading = 124.(b) IQ = 124, reading = 72.(c) IQ = 124, reading = 10.
In a scatterplot of the average price of a barrel of oil and the average retail price of a gallon of gasoline, you expect to see(a) a positive association.(b) very little association.(c) a negative association.
You have data for many years on the average price of a barrel of oil and the average retail price of a gallon of unleaded regular gasoline. When you make a scatterplot, the explanatory variable on the x axis(a) is the price of oil.(b) is the price of gasoline.(c) can be either oil price or gasoline
Grading managers. In Exercise 3.44, we saw that Ford Motor Company once APPLET •••graded its managers in such a way that the top 10% received an A grade, the bottom 10% a C, and the middle 80% a B. Let’s suppose that performance scores follow a Normal distribution. How many standard
Where are the quartiles? How many standard deviations above and below the APPLET •••mean do the quartiles of any Normal distribution lie? (Use the standard Normal distribution to answer this question.)
How accurate is 68–95–99.7? The 68–95–99.7 rule for Normal distributions is a APPLET •••useful approximation. To see how accurate the rule is, drag one flag across the other so that the applet shows the area under the curve between the two flags.(a) Place the flags one standard
Are the data Normal? Soil penetrability. Table 2.5 (page 65) gives data on the penetrability of soil at each of three levels of compression. We might expect the penetrability of specimens of the same soil at the same level of compression to follow a Normal distribution. Make stemplots of the data
Are the data Normal? Monsoon rains. Here are the amounts of summer monsoon rainfall (millimeters) for India in the 100 years 1901 to 2000:12 722.4 792.2 861.3 750.6 716.8 885.5 777.9 897.5 889.6 935.4 736.8 806.4 784.8 898.5 781.0 951.1 1004.7 651.2 885.0 719.4 866.2 869.4 823.5 863.0 804.0 903.1
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