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Statistics Concepts And Controversies 10th Edition David S. Moore, William I. Notz - Solutions

14.18 Long eyelashes. False eyelashes are sometimes worn in an effort to extend the length of an individual’s natural eyelashes. Research suggests, however, that our natural eyelash length is proportional to the width of our eye. To better understand how eye width length (in centimeters, or cm)
14.17 Outliers and correlation. In Figure 14.13, the point marked A is an outlier. Will removing the outlier increase or decrease r? Why?
14.16 Comparing correlations. Which of Figures 14.2, 14.12, and 14.13 has a correlation closer to 0? Explain your answer.
14.15 Calories and salt in hot dogs. Is the correlation r for the data in Figure 14.13 near −1, clearly negative but not near −1, near 0, clearly positive but not near 1, or near 1? Explain your answer.
14.14 The endangered manatee. Is the correlation r for the data in Figure 14.12 near −1, clearly negative but not near −1, near 0, clearly positive but not near 1, or near 1? Explain your answer.
14.13 Calories and salt in hot dogs. Figure 14.13 (page 335) shows the calories and sodium content in 17 brands of hot dogs. Describe the overall pattern of these data. In what way is the point marked A unusual?Figure 14.13 Calories and sodium content for 17 brands of hot dogs, Exercise 14.13.The
14.12 The endangered manatee. Manatees are large, gentle, slow-moving creatures found along the coast of Florida. Many manatees are injured or killed by boats. Figure 14.12 is a scatterplot of the number of manatee deaths by boats versus the number of boats registered in Florida (in thousands) for
14.11 Living on campus. A February 2, 2008, article in the Columbus Dispatch reported a study on the distances students lived from campus and average grade point average (GPA).Here is a summary of the results:Residence Avg. GPA Residence hall 3.33 Walking distance 3.16 Near campus, long walk or
14.10 Measuring mice. For a biology project, you measure the tail length (millimeters) and weight (grams) of 10 mice.a. Explain why you expect the correlation between tail length and weight to be positive.b. If you measured tail length in centimeters rather than millimeters, would you expect the
14.9 What number can I be?a. What are all the values that a correlation r can possibly take?b. What are all the values that a standard deviation s can possibly take?c. What are all the values that a mean x¯ can possibly take?
14.8 Correlation and scatterplots If the points in a scatterplot are very tightly clustered around a straight line, the correlation must bea. close to 0.b. close to +1.c. close to −1.d. close to either +1 or −1.Chapter 14 Exercises
14.7 Correlation Which of the following is true of the correlation r?a. It cannot be greater than 1 or less than −1.b. It measures the strength of the straight-line relationship between two quantitative variables.c. A correlation of +1 or −1 can only happen if there is a perfect straight-line
14.6 Interpreting scatterplots Which of the following patterns might one observe in a scatterplot?a. The points in the plot follow a curved pattern.b. The points in the plot group into different clusters.c. One or two points are clear outliers.d. All of the above.
14.5 Interpreting scatterplots If the points in a scatterplot of two variables slope downward from left to right, we say the direction of the relationship between the variables isa. positive.b. negative.c. strong.d. weak.
14.4 Creating scatterplots When creating a scatterplot,a. always put the categorical variable on the horizontal axis.b. always put the categorical variable on the vertical axis.c. if you have an explanatory variable, put it on the horizontal axis.d. if you have a response variable, put it on the
3. Write a paragraph, in language that someone who knows no statistics would understand, explaining why comparing states on the basis of average SAT scores alone would be misleading as a way of comparing the quality of education in the states.
2. The plot shows two groups of states. In one group, fewer than 20% took the SAT. In the other, at least 26% took the exam and the average scores tend to be lower. There are two common college entrance exams, the SAT and the ACT. In ACT states, only students applying to selective colleges take the
1. Describe the overall pattern in words. Is the association positive or negative? Is the relationship strong?
13.35 High IQ scores. Scores on the Wechsler Adult Intelligence Scale for the 20 to 34 age group are approximately Normally distributed with mean 110 and standard deviation 15.How high must a person score to be in the top 5% of all scores?
13.34 Women’s heights. The heights of adult women are approximately Normal with mean 69.2 inches and standard deviation 2.5 inches. How tall are the tallest 10% of women? (Use the closest percentile that appears in Table B.)
13.33 Locating the quartiles. The quartiles of any distribution are the 25th and 75th percentiles. About how many standard deviations from the mean are the quartiles of any Normal distribution?
13.32 The stock market. The annual rate of return on stock indexes (which combine many individual stocks) is very roughly Normal. Since 1945, the Standard & Poor’s 500 index has had a mean yearly return of 12.5%, with a standard deviation of 17.8%. Take this Normal distribution to be the
13.31 Japanese IQ scores. The Wechsler Intelligence Scale for Children is used (in several languages) in the United States and Europe. Scores in each case are approximately Normally distributed with mean 100 and standard deviation 15. When the test was standardized in Japan, the mean was 111. To
13.30 Are we getting smarter? When the Stanford-Binet IQ test came into use in 1932, it was adjusted so that scores for each age group of children followed roughly the Normal distribution with mean 100 and standard deviation 15. The test is readjusted from time to time to keep the mean at 100. If
13.29 SAT ERW scores. In 2018, the average performance of college-bound seniors on the Evidence-Based Reading and Writing (ERW) portion of the SAT followed a Normal distribution with mean 522 and standard deviation 114. The mean for the SAT Math portion was 542. What percentage of scores on the SAT
13.28 800 on the SAT. It is possible to score higher than 800 on the SAT, but scores above 800 are reported as 800. (That is, a student can get a reported score of 800 without a perfect paper.) In 2018, the scores of college-bound seniors SAT Math test followed a Normal distribution with mean 542
13.27 More NCAA rules. For Division I athletes the NCAA uses a sliding scale, based on both core GPA and the combined Mathematics and Critical Reading SAT score, to determine eligibility to compete in the first year of college. For athletes with a core GPA of 3.0, a score of at least 620 on the
13.26 NCAA rules for athletes. The National Collegiate Athletic Association (NCAA)requires Division II athletes to get a combined score of at least 820 on the Mathematics and Critical Reading sections of the SAT exam in order to compete in their first college year. In 2018, the combined scores of
13.25 Cholesterol. Low-density lipoprotein, or LDL, is the main source of cholesterol buildup and blockage in the arteries. This is why LDL is known as “bad cholesterol." LDL is measured in milligrams per deciliter of blood, or mg/dL. In a population of adults at risk for cardiovascular problems,
13.24 Sleep. The distribution of hours of sleep per school night, among high school seniors, is found to be Normally distributed, with a mean of 6.6 hours and a standard deviation of 1.3 hours. Use this information and the 68–95–99.7 rule to answer the following questions.a. What percentage of
13.23 Heights of adults. The mean height of men is about 69.2 inches. Women that age have a mean height of about 63.7 inches. Do you think that the distribution of heights for all adults is approximately Normal? Explain your answer.
13.22 Heights of men and women. The heights of women are approximately Normal with mean 63.7 inches and standard deviation 2.5 inches. The heights of men have mean 69.2 inches and standard deviation 2.5 inches. What percentage of women are taller than a man of average (mean) height?
13.21 More on men’s heights. The distribution of heights of men is approximately Normal with mean 69.2 inches and standard deviation 2.5 inches. Use the 68–95–99.7 rule to answer the following questions.a. What percentage of men are shorter than 61.7 inches?b. Between what heights do the
13.20 Men’s heights. The distribution of heights of men is approximately Normal with mean 69.2 inches and standard deviation 2.5 inches. Sketch a Normal curve on which this mean and standard deviation are correctly located. (Hint: Draw the curve first, locate the points where the curvature
13.19 Comparing IQ scores. The Wechsler Adult Intelligence Scale (WAIS) is an IQ test.Scores on the WAIS for the 20 to 34 age group are approximately Normally distributed with mean 110 and standard deviation 15. Scores for the 60 to 64 age group are approximately Normally distributed with mean 90
13.18 Great hitters then and now. Three landmarks of baseball achievement are Ty Cobb’s batting average of .420 in 1911, Ted Williams’s .406 in 1941, and George Brett’s .390 in 1980. These batting averages cannot be compared directly because the distribution of major league batting averages
13.17 Horse pregnancies. Bigger animals tend to carry their young longer before birth. The length of horse pregnancies from conception to birth varies according to a roughly Normal distribution with mean 336 days and standard deviation 3 days. Use the 68–95–99.7 rule to answer the following
13.16 A Normal curve. What are the mean and standard deviation of the Normal curve in Figure 13.14?Figure 13.14 What are the mean and standard deviation of this Normal density curve? For Exercise 13.16.The bell-shaped curve originates from 3.4 on the horizontal axis, rises, peaks above 10 on the
13.15 Length of pregnancies. The length of human pregnancies from conception to birth varies according to a distribution that is approximately Normal with mean 266 days and standard deviation 16 days. Use the 68–95–99.7 rule to answer the following questions.a. Almost all (99.7%) pregnancies
13.14 What percentage of all students have IQ scores below 80? None of the 80 adults in our sample had scores this low. Are you surprised at this? Why?
13.13 What percentage of IQ scores for all adults are more than 100?
13.12 Between what values do the IQ scores of 68% of all adults lie?
13.11 Random numbers. If you ask a computer to generate “random numbers” between 0 and 5, you will get observations from a uniform distribution. Figure 13.12 shows the density curve for a uniform distribution. This curve takes the constant value 0.2 between 0 and 5 and is zero outside that
13.10 Mean and median. Figure 13.11 shows density curves of several shapes. Briefly describe the overall shape of each distribution. Two or more points are marked on each curve.The mean and the median are among these points. For each curve, which point is the median and which is the mean?Figure
13.9 Density curvesa. Sketch a density curve that is strongly skewed to the left.b. Sketch a density curve that is symmetric but has a shape different from that of the Normal curves.
13.8 Reading test scores. A standardized reading test is given to fifth-grade students. Scores on this test are Normally distributed, with a mean of 32 points and a standard deviation of 8 points. When Corey gets his test results, he is told that his score is at the 95th percentile.What does this
13.7 More on pulse rates. Let’s again assume that the resting pulse rates for healthy adults follow a Normal distribution with a mean of 69 beats per minute and a standard deviation of 9.5 beats per minute. When converted to a standard score, Adam’s pulse rate becomes −.How should this
13.6 Pulse rates. Suppose that resting pulse rates for healthy adults are found to follow a Normal distribution, with a mean of 69 beats per minute and a standard deviation of 9.5 beats per minutes. If Bonnie has a pulse rate of 78.5 beats per minute, this means thata. Approximately 32% of adults
13.5 The mean and median. Which of the following is an incorrect statement?a. If a density curve is skewed to the right, the mean will be larger than the median.b. In a symmetric density curve, the mean is equal to the median.c. The median is the balance point in a density curve.d. The mean of a
13.4 Density curves. One characteristic of a density curve is that there is a specific total area under the curve. What is this area equal to?a. Exactly 1.b. Approximately 1.c. It depends on what is being measured.d. It depends on whether the distribution is Normal.
2. There was a time when 98.6 degrees Fahrenheit was considered the average body temperature. Given what you know about the distribution of body temperatures given in Figures 13.2 and 13.3, what percentage of individuals would you expect to have body temperatures greater than 98.6 degrees
1. According to the 68-95-99.7 rule, 68% of body temperatures fall between what two values? Between what two values do 95% of body temperatures fall?
12.39 What graph to draw? We now understand three kinds of graphs to display distributions of quantitative variables: histograms, stemplots, and boxplots. Give an example(just words, no data) of a situation in which you would prefer that graphing method.
12.38 Making colleges look good. Colleges announce an “average” SAT score for their entering freshmen. Usually the college would like this “average” to be as high as possible. A New York Times article noted, “Private colleges that buy lots of top students with merit scholarships prefer
12.37 Raising pay. Suppose that the teachers in the previous exercise each receive a 5%raise. The amount of the raise will vary from $2000 to $3500, depending on present salary.Will a 5% across-the-board raise increase the variability of the distribution as measured by the distance between the
12.36 Raising pay. A school system employs teachers at salaries between $40,000 and$70,000. The teachers’ union and the school board are negotiating the form of next year’s increase in the salary schedule. Suppose that every teacher is given a flat $3000 raise.a. How much will the mean salary
12.35 x¯ and s are not enough. The mean x¯ and standard deviation s measure center and variability 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
12.34 A contest. This is a standard deviation contest. You must choose four numbers from the whole numbers 0 to 9, with repeats allowed.a. Choose four numbers that have the smallest possible standard deviation.b. Choose four numbers that have the largest possible standard deviation.c. Is more than
12.33 Cars and SUVs. Use the mean and standard deviation to compare the gas mileages of mid-size cars (Table 11.2, page 261) and SUVs (Exercise 12.28). Do these numbers catch the main points of your more detailed comparison in Exercise 12.28?
12.32 What s measures. Add 2 to each of the numbers in data set (a) in the previous exercise. The data are now 6 4 6 4 6 4.a. Use a calculator to find the mean and standard deviation and compare your answers with those for data set part (a) in the previous exercise. How does adding 2 to each number
12.31 What s measures. Use a calculator to find the mean and standard deviation of these two sets of numbers:a. 4 2 4 2 4 2b. 5 5 5 1 1 1 Which data set is more variable?
12.30 Finding the standard deviation. The level of various substances in the blood influences our health. Here are measurements of the level of phosphate in the blood of a patient, in milligrams of phosphate per deciliter of blood, made on six consecutive visits to a clinic:5.6 5.2 4.6 4.9 5.7 6.4
12.29 How many calories in a hot dog? Some people worry about how many calories they consume. Consumer Reports magazine, in a story on hot dogs, measured the calories in 20 brands of beef hot dogs, 17 brands of meat hot dogs, and 17 brands of poultry hot dogs. Here is computer output describing the
12.28 Do SUVs waste gas? Table 11.2 (page 261) gives the highway fuel consumption (in miles per gallon) for 31 model year 2015 midsized cars. You found the five-number summary for these data in Exercise 12.14. Here are the highway gas mileages for 26 four-wheel-drive model year 2015 sport utility
12.27 State SAT scores. We want to compare the distributions of average SAT Math and Evidence-Based Reading and Writing (ERW) scores for the states and the District of Columbia. We enter these data into a computer with the names SATM for Math scores and SATERW for Evidence-Based Reading and Writing
12.26 Mean or median? You are planning a party and want to know how many cans of soda to buy. A genie offers to tell you either the mean number of cans guests will drink or the median number of cans. Which measure of center should you ask for? Why? To make your answer concrete, suppose there will
12.25 Mean or median? Which measure of center, the mean or the median, should you use in each of the following situations? Why?a. Middletown is considering imposing an income tax on citizens. The city government wants to know the average income of citizens so that it can estimate the total tax
12.24 Highly paid athletes. A news article reported that of the 446 players on National Basketball Association rosters in 2015, only 146 made more than $5 million. The article also stated that the average NBA salary in 2015 was $5.2 million. Was $5.2 million the mean or median salary for NBA
12.23 State SAT scores. Figure 12.9 is a histogram of the average scores on the SAT Mathematics exam for college-bound senior students in the 50 states and the District of Columbia in 2018. The distinctive overall shape of this distribution implies that a single measure of center such as the mean
12.22 Immigrants in the eastern states. New York and Florida are high outliers in the distribution of the previous exercise. Find the mean and the median for these data with and without New York and Florida. Which measure changes more when we omit the outliers?
12.21 Immigrants in the eastern states. Here are the number of legal immigrants (in thousands) who settled in each state east of the Mississippi River in 2017:Alabama 3.8 New Hampshire 2.3 Connecticut 11.9 New Jersey 54.4 Delaware 2.2 New York 139.4 Florida 127.6 North Carolina 21.1 Georgia 26.2
12.20 The statistics of writing style. Here are data on the percentages of words of 1 to 15 letters used in articles in Popular Science magazine. Exercise 11.16 (page 261) asked you to make a histogram of these data.Length: 1 2 3 4 5 6 7 8 Percent: 3.6 14.8 18.7 16.0 12.5 8.2 8.1 5.9 Length: 9 10
12.19 The Super Bowl MVP. Figure 11.12 (page 259) is a histogram of the ages of players who have been named a Super Bowl Most Valuable Player (MVP) for the first 52 Super Bowl Games. The classes for Figure 11.12 are 22–23.5, 23.6–25, and so on.a. What is the position of each number in the
12.18 Returns on common stocks. Example 5 informs us that financial theory uses the mean and standard deviation to describe the returns on investments. Figure 11.13 (page 260) is a histogram of the returns of all New York Stock Exchange common stocks in one year. Are the mean and standard deviation
12.17 How many calories does a hot dog have? Consumer Reports magazine presented the following data on the number of calories in a hot dog for each of 17 brands of meat hot dogs:173 191 182 190 172 147 146 139 175 136 179 153 107 195 135 140 138 Make a stemplot if you did not already do so in
12.16 The richest 5%. The distribution of individual incomes in the United States is strongly skewed to the right. In 2016, if we only look at the incomes of the top 5% of Americans, the mean and median incomes of the individuals in the top 5% were $215,000 and $375,000.Which of these numbers is
12.15 Twins money. Table 11.4 (page 262) gives the salaries of the Minnesota Twins baseball team. What shape do you expect the distribution to have? Do you expect the mean salary to be close to the median, clearly higher, or clearly lower? Verify your choices by making a graph and calculating the
12.14 Gas mileage. Table 11.2 (page 261) gives the highway gas mileages for some model year 2015 midsized cars.a. Make a stemplot of these data if you did not do so in Exercise 11.13.b. Find the five-number summary of gas mileages. Which cars are in the bottom quarter of gas mileages?c. The
12.13 Where are the young more likely to live? Figure 11.11 (page 258) is a stemplot of the percentage of residents aged 18 to 34 in each of the 50 states. The stems are whole percents and the leaves are tenths of a percent.a. The shape of the distribution suggests that the mean will be about the
12.12 College tuition. Figure 11.7 (page 254) is a stemplot of the tuition charged by 114 colleges in Illinois. The stems are thousands of dollars and the leaves are hundreds of dollars.For example, the highest tuition is $53,600 and appears as leaf 6 on stem 53.a. Find the five-number summary of
12.11 Rich magazine readers. Seattle Magazine reports that the average income of its readers is $240,000. Is the median wealth of these readers greater or less than $240,000?Why?
12.10 What’s the average? The Census Bureau website gives several choices for “average income” in its historical income data. In 2017, the median income of American households was $68,145. The mean household income was $93,453. The median income of families was$75,938, and the mean family
12.9 Median income. You read that the median income of U.S. households in 2017 was$68,145. Explain in plain language what “the median income” is.
12.8 Describing distributions Which of the following should you use to describe a distribution that is skewed?a. The five-number summaryb. The mean, the first quartile, and the third quartilec. The mean and standard deviationd. The median and standard deviation
12.7 The five-number summary Which of the following is a graph of the five-number summary?a. A histogramb. A stemplotc. A boxplotd. A bar graph
12.6 Standard deviation Which of the following statements is true of the standard deviation?a. Removing an outlier will decrease the standard deviation.b. Removing an outlier will increase the standard deviation.c. It is the difference between the first and third quartile.d. It is the difference
12.5 Median The median of the three numbers, 1, 2, and 15, is equal toa. 1.b. 2.c. 5.d. 6.
12.4 Mean The mean of the three numbers, 1, 2, and 15, is equal toa. 1.b. 2.c. 5.d. 6.
3. Do people with more education earn more than people with less education? Discuss.
2. From the distribution given in the tables, can you find the (approximately) first and third quartiles?
1. What are the median incomes for people 25 years old and older who are high school graduates only, have some college but no degree, have a bachelor’s degree, have a master’s degree, and have a doctorate degree? At the bottom of the table, you will find median earnings in dollars.
11.24 What’s wrong? The Economic Research Service (ERS) from the U.S. Department of Agriculture (USDA) uses information from different retail establishments to provide estimates of the average price per pound (in dollars) of different fruits and vegetables. These prices are used when publishing
11.23 When it rains, it pours. On July 25 to 26, 1979, 42.00 inches of rain fell on Alvin, Texas. That’s the most rain ever recorded in Texas for a 24-hour period. Table 11.6 gives the maximum precipitation ever recorded in 24 hours (through 2010) at any weather station in each state. The record
11.22 Back-to-back stemplot. The current major league single-season home run record is held by Barry Bonds of the San Francisco Giants. Here are Bonds’s home run counts for 1986 to 2007:16 25 24 19 33 25 34 46 37 33 42 40 37 34 49 73 46 45 45 5 26 28 A back-to-back stemplot helps us compare two
11.21 Babe Ruth’s home runs. Here are the numbers of home runs that Babe Ruth hit in his 15 years with the New York Yankees, 1920 to 1934:54 59 35 41 46 25 47 60 54 46 49 46 41 34 22 Make a stemplot of these data. Is the distribution roughly symmetric, clearly skewed, or neither? About how many
11.20 The changing age distribution of the United States. The distribution of the ages of a nation’s population has a strong influence on economic and social conditions. Table 11.5 shows the age distribution of U.S. residents in 1950 and 2050, in millions of persons. The 1950 data come from that
11.19 How many calories does a hot dog have? Consumer Reports magazine presented the following data on the number of calories in a hot dog for each of 17 brands of meat hot dogs:173 191 182 190 172 147 146 139 175 136 179 153 107 195 135 140 138 Make a stemplot of the distribution of calories in
11.18 The Asian population in the eastern states. When the 2010 census was published, it was reported that the Asian population grew faster than any other race group in the United States during the decade from 2000 to 2010. Here are the percentages of the population who are of Asian origin in each
11.17 What’s my shape? There are 30 teams in the National Basketball Association (NBA), and each team has a team payroll. The team payroll consists of the total amount of money available to pay all players on the team. As an example, in the 2018–19 season, the LA Lakers had a team payroll of
11.16 The statistics of writing style. Numerical data can distinguish different types of writing, and sometimes even individual authors. Here are data collected by students on the percentages of words of 1 to 15 letters used in articles in Popular Science magazine:Length: 1 2 3 4 5 Percent: 3.6

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