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Statistics Concepts And Controversies 7th Edition David S Moore, William I Notz - Solutions

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 the mean,
Raising pay. Suppose that the teachers in the previous exercise each receive a 5% raise. The amount of the raise will vary from $1500 to $3000, depending on present salary.Will a 5% across-the-board raise increase the spread of the distribution as measured by the distance between the quartiles? Do
Raising pay. A school system employs teachers at salaries between$30,000 and $60,000. 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 $1000 raise.(a) How much will the mean salary
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
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 one
Cars and SUVs. Use the mean and standard deviation to compare the gas mileages of sedans (Table 11.2, page 233) and SUVs (Exercise 12.23).Do these numbers catch the main points of your more detailed comparison in Exercise 12.23?
What s measures. Add 2 to each of the numbers in data set (a) in the previous exercise. The data are now 6 2 3 6 5 8.(a) Use a calculator to find the mean and standard deviation and compare your answers with those for data set (a) in the previous exercise. How does adding 2 to each number change
What s measures. Use a calculator to find the mean and standard deviation of these two sets of numbers:(a)4 0 1 4 3 6(b)5 3 1 3 4 2 Which data set is more spread out?
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 6 consecutive visits to a clinic:5.6 5.2 4.6 4.9 5.7 6.4 A graph
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 beef
Do SUVs waste gas? Table 11.2 (page 233) gives the highway fuel consumption(in miles per gallon) for 31 model year 2008 sedans. You found the five-number summary for these data in Exercise 12.9. Here are the highway gas mileages for 26 four-wheel-drive model year 2008 sport utility vehicles:Model
State SAT scores. We want to compare the distributions of average SAT Math and Verbal scores for the states and the District of Columbia. We enter these data into a computer with the names SATM for Math scores and SATV for Verbal scores. Here is output from the statistical software package
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 be 30
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 base.(b)
Highly paid athletes. A news article reports that of the 411 players on National Basketball Association rosters in February 1998, only 139 “made more than the league average salary” of $2.36 million. Is $2.36 million the mean or median salary for NBA players? How do you know?
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?
Immigrants in the eastern states. Here are the number of legal immigrants(in thousands) who settled in each state east of the Mississippi River from 2000 to 2005:Alabama 46.0 Connecticut 94.4 Delaware 20.1 Florida 727.9 Georgia 253.5 Illinois 349.1 Indiana 83.0 Kentucky 34.9 Maine 6.7 Maryland
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 11.11 (page 234) asked you to make a histogram of these data.Length: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Percent: 3.6 14.8 18.7 16.0 12.5 8.2 8.1 5.9
Minority students in engineering. Figure 11.11 (page 231) is a histogram of the number of minority students (black, Hispanic, Native American)who earned doctorate degrees in engineering from each of 152 universities in the years 2000 through 2002. The classes for Figure 11.11 are 1–5, 6–10, and
Returns on common stocks. Example 5 informs us that financial theory uses the mean and standard deviation to describe the returns on investments.Figure 11.12 (page 232) is a histogram of the returns of all New York Stock Exchange common stocks in one year. Are the mean and standard deviation
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 and find the five-number summary. The
The richest 1%. The distribution of individual incomes in the United States is strongly skewed to the right. In 2004, the mean and median incomes of the top 1% of Americans were $315,000 and $1,259,700. Which of these numbers is the mean and which is the median? Explain your reasoning.
Yankee money. Table 11.4 (page 234) gives the salaries of the New York Yankees 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 mean
Gas mileage. Table 11.2 (page 233) gives the highway gas mileages for model year 2008 sedans.(a) Make a stemplot of these data if you did not do so in Exercise 11.8.(b) Find the five-number summary of gas mileages. Which cars are in the bottom quarter of gas mileages?(c) The stemplot shows a fact
Where are the young more likely to live? Figure 11.10 (page 231) is a stemplot of the percentage of residents aged under 18 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 larger than the
College tuition. Figure 11.7 (page 228) is a stemplot of the tuition charged by 121 colleges in Illinois. The stems are thousands of dollars and the leaves are hundreds of dollars. For example, the highest tuition is $30,700 and appears as leaf 7 on stem 30.(a) Find the five-number summary of
Rich magazine readers. The business magazine Forbes reports (July 5, 1999) that the median household wealth of its readers is $956,000.(a) Is the mean wealth of these households greater or less than $956,000? Why?(b) The data were reported by a sample of Forbes readers contacted by telephone.We
What’s the average? The Census BureauWeb site gives several choices for “average income” in its historical income data. In 2006, the median income of American households was $48,201. The mean household income was $66,570.The median income of families was $58,407, and the mean family income
Median income. You read that the median income of U.S. households in 2006 was $48,201. Explain in plain language what “the median income” is.
Hank Aaron. Here are Aaron’s home run counts for his 23 years in baseball.13 27 26 44 30 39 40 34 45 44 24 32 44 39 29 44 38 47 34 40 20 12 10 Find the mean and standard deviation of the number of home runs Aaron hit in each season of his career. How do the mean and median compare?
Babe Ruth. Here are Babe Ruth’s home run counts for his 22 years in Major League Baseball, arranged in order from smallest to largest:0 2 3 4 6 11 22 25 29 34 35 41 41 46 46 46 47 49 54 54 59 60 Draw a boxplot of this distribution. How does it compare with those of Barry Bonds and Hank Aaron in
Babe Ruth. Prior to Hank Aaron, Babe Ruth was the holder of the career record. Here are Ruth’s home run counts for his 22 years in Major League Baseball, arranged in order from smallest to largest:0 2 3 4 6 11 22 25 29 34 35 41 41 46 46 46 47 49 54 54 59 60 Find the median, first quartile, and
Web-based exercise. The all-time home run leader prior to 2007 was Hank Aaron. You can find his career statistics at the Web site www.baseball-reference.com. Make a stemplot of the number of home runs that Hank Aaron hit in his career. Is the distribution roughly symmetric, clearly skewed, or
When it rains, it pours. On July 6, 1994, 21.10 inches of rain fell on Americus, Georgia. That’s the most rain ever recorded in Georgia for a 24-hour period. Table 11.6 gives the maximum precipitation ever recorded in 24 hours(through 1998) at any weather station in each state. The record amount
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
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 home
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 2075, in millions of persons. The 1950 data come from that
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 meat hot
Asians in the eastern states. Here are the percentages of the population who are of Asian origin in each state east of the Mississippi River in 2006:State Percent State Percent State Percent Alabama 1.0 Connecticut 3.3 Delaware 2.9 Florida 2.2 Georgia 2.7 Illinois 4.2 Indiana 1.3 Kentucky 0.9 Maine
What’s my shape? Do you expect the distribution of the total player payroll for each of the 30 teams in Major League Baseball to be roughly symmetric, clearly skewed to the right, or clearly skewed to the left? Why?
Skewed left. Sketch a histogram for a distribution that is skewed to the left. Suppose that you and your friends emptied your pockets of coins and recorded the year marked on each coin. The distribution of dates would be skewed to the left. Explain why.Chapter 11 Exercises 235
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 6 7 8 9 10 11 12 13 14
Yankee money. Table 11.4 gives the salaries of the players on the New York Yankees baseball team as of the opening day of the 2007 season. Make a histogram of these data. Is the distribution roughly symmetric, skewed to the right, or skewed to the left? Explain.
The obesity epidemic. Medical authorities describe the spread of obesity in the United States as an epidemic. Table 11.3 gives the percentage of adults who were obese in each of the 50 states in 2006. Display the distribution in a graph and briefly describe its shape, center, and spread.TABLE 11.2
Automobile fuel economy. Government regulations require automakers to give the city and highway gas mileages for each model of car. Table 11.2 gives the highway mileages (miles per gallon) for 31 model year 2008 sedans.Make a stemplot of the highway gas mileages of these cars. What can you say
Histogram or stemplot? Explain why we prefer a histogram to a stemplot for describing the returns on 1528 common stocks.
Returns on common stocks. The total return on a stock is the change in its market price plus any dividend payments made. Total return is usually expressed as a percentage of the beginning price. Figure 11.12 is a histogram of the distribution of total returns for all 1528 common stocks listed on
Where do the young live? Figure 11.10 is a stemplot of the percentage of residents aged under 18 in each of the 50 states in 2006. As in Figure 11.6 (page 227) for older residents, the stems are whole percents and the leaves are tenths of a percent.(a) Utah has the largest percentage of young
85-year-olds and older. Figure 11.5 is a histogram of the percentages of residents aged 85 and older in the 50 states in 2006. Describe the shape, center, and spread of this distribution. Are there any outliers?
15- to 44-year-olds. Below are the percentages of residents between the ages of 15 and 44 in the 50 states in 2006.State Percent State Percent Alabama 41.0 Montana 39.1 Alaska 45.0 Nebraska 41.2 Arizona 42.3 Nevada 43.0 Arkansas 40.8 New Hampshire 41.1 California 44.4 New Jersey 41.3 Colorado 44.1
Web-based exercise. One of the best ways to grasp the idea of probability is to watch the proportion of trials on which an outcome occurs gradually settle down at the outcome’s probability. Computer simulations can show this. Go to the Statistics: Concepts and Controversies Web site,
Web-based exercise. Search the Web to see if you can find an example of a misuse or misstatement of the law of averages. Explain why the statement you find is incorrect. (We found some examples by doing a Google search on the phrase “law of averages.”)
What probability doesn’t say. The probability of a head in tossing a coin is 1/2. This means that as we make more tosses, the proportion of heads will eventually get close to 0.5. It does not mean that the count of heads will get close to 1/2 the number of tosses. To see why, imagine that the
Reacting to risks. National newspapers such as USA Today and the New York Times carry many more stories about deaths from airplane crashes than about deaths from automobile crashes. Auto accidents killed about 45,000 people in the United States in 2006. Crashes of all scheduled air carriers,
Reacting to risks. The probability of dying if you play high school football is about 10 per million each year you play. The risk of getting cancer from asbestos if you attend a school in which asbestos is present for 10 years is about 5 per million. If we ban asbestos from schools, should we also
An unenlightened gambler.(a) A gambler knows that red and black are equally likely to occur on each spin 392 CHAPTER 17 Thinking about Chance of a roulette wheel. He observes five consecutive reds occur and bets heavily on black at the next spin. Asked why, he explains that black is “due by the
Snow coming. A meteorologist, predicting above-average snowfall this winter, says, “First, in looking at the past few winters, there has been belowaverage snowfall. Even though we are not supposed to use the law of averages, we are due.” Do you think that “due by the law of averages” makes
The “law of averages.” The baseball player Ichiro Suzuki gets a hit about 1/3 of the time over an entire season. After he has failed to hit safely in nine straight at-bats, the TV commentator says, “Ichiro is due for a hit by the law of averages.” Is that right? Why?
In the long run. Probability works not by compensating for imbalances but by overwhelming them. Suppose that the first 10 tosses of a coin give 10 tails and that tosses after that are exactly half heads and half tails. (Exact balance is unlikely, but the example illustrates how the first 10
Nash’s free throws. The basketball player Steve Nash is the all-time career free throw shooter among active players. He makes about 90% of his free throws. In today’s game, Nash misses his first two free throws. The TV commentator says, “Nash’s technique looks out of rhythm today.”
Surprising? You are getting to know your new roommate, assigned to you by the college. In the course of a long conversation, you find that both of you have sisters named Deborah. Should you be surprised? Explain your answer.
Playing Pick 4. The Pick 4 games in many state lotteries announce a four-digit winning number each day. The winning number is essentially a fourdigit group from a table of random digits. You win if your choice matches the winning digits, in exact order. The winnings are divided among all players
Personal random numbers? Ask several of your friends (at least 10 people) to choose a four-digit number “at random.” How many of the numbers chosen start with 1 or 2? How many start with 8 or 9? (There is strong evidence that people in general tend to choose numbers starting with low digits.)
Personal probability? When there are few data, we often fall back on personal probability. There had been just 24 space shuttle launches, all successful, before the Challenger disaster in January 1986. The shuttle program management thought the chances of such a failure were only 1 in 100,000.(a)
Personal probability versus data. Give an example in which you would rely on a probability found as a long-term proportion from data on many trials. Give an example in which you would rely on your own personal probability.
Marital status. The probability that a randomly chosen 50-yearold woman is divorced is about 0.18. This probability is a long-run proportion based on all the millions of women aged 50. Let’s suppose that the proportion stays at 0.18 for the next 30 years. Bridget is now 20 years old and is not
Will you have an accident? The probability that a randomly chosen driver will be involved in an accident in the next year is about 0.2. This is based on the proportion of millions of drivers who have accidents. “Accident”includes things like crumpling a fender in your own driveway, not just
Winning a baseball game. Over the period from 1967 to 2007 the champions of baseball’s two major leagues won 62% of their home games during the regular season. At the end of each season, the two league champions meet in the baseball World Series. Would you use the results from the regular season
From words to probabilities. 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
Two pairs. You read in a book on poker that the probability of being dealt two pairs in a five-card poker hand is 1/21. Explain in simple language what this means.
Tossing a thumbtack. Toss a thumbtack on a hard surface 100 times.How many times did it land with the point up? What is the approximate probability of landing point up?
How many tosses to get a head? When we toss a penny, experience shows that the probability (long-term proportion) of a head is close to 1/2. Suppose now that we toss the penny repeatedly until we get a head. What is the probability that the first head comes up in an odd number of tosses (1, 3, 5,
Random digits. The table of random digits (Table A) was produced by a random mechanism that gives each digit probability 0.1 of being a 0. What proportion of the first 200 digits in the table are 0s? This proportion is an estimate, based on 200 repetitions, of the true probability, which in this
Pennies falling over. You may feel that it is obvious that the probability of a head in tossing a coin is about 1/2 because the coin has two faces. Such opinions are not always correct. The previous exercise asked you to spin a penny rather than toss it—that changes the probability of a head. Now
Pennies spinning. Hold a penny upright on its edge under your forefinger on a hard surface, then snap it with your other forefinger so that it spins for some time before falling. Based on 50 spins, estimate the probability of heads.
Coin tossing and the law of averages. The author C. S. Lewis once wrote the following, referring to the law of averages: “If you tossed a coin a billion times, you could predict a nearly equal number of heads and tails.” Is this a correct statement of the law of averages? If not, how would you
Coin tossing and randomness. Toss a coin 10 times and record heads (H) or tails (T) on each toss. Which of these outcomes is most probable? Least probable?HTHTTHHTHT TTTTTHHHHH HHHHHHHHHH
Web-based exercise. The best way to grasp how the correlation reflects the pattern of the points on a scatterplot is to use an “applet”that allows you to plot and move data points and watch the correlation change. Go to the Statistics: Concepts and Controversies Web site,
Web-based exercise. A popular saying in golf is “You drive for show but you putt for dough.” You can find this season’s Professional Golfers Association (PGA) tour statistics at the PGA tour Web site:www.pgatour.com/stats. You can also find these statistics at the ESPN Web site:
Why so small? Make a scatterplot of the following data:x 1 2 3 4 9 10 y 10 3 3 5 9 11 Use your calculator to show that the correlation is about 0.5. What feature of the data is responsible for reducing the correlation to this value despite a strong straight-line association between x and y in most
How many corn plants are too many? How much corn per acre should a farmer plant to obtain the highest yield? To find the best planting rate, do an experiment: plant at different rates on several plots of ground and measure the harvest. Here are data from such an experiment:Plants per acre Yield
Take me out to the ball game. What is the relationship between the price charged for a hot dog and the price charged for a 16-ounce soda in Major League Baseball stadiums? Table 14.2 gives some data. Make a scatterplot appropriate for showing how soda price helps explain hot dog price. Describe the
Investment diversification. A mutual funds company’s newsletter says, “A well-diversified 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
Guess the correlation. For each of the following pairs of variables, would you expect a substantial negative correlation, a substantial positive correlation, or a small correlation?(a) The cost of an Internet supplier service and the download speed provided by the service.(b) The horsepower of new
Guess the correlation. Measurements in large samples show that the correlation(a) between SAT scores and college GPA is about .(b) between the IQ and the GPA of seventh-grade students is about .(c) between the GPA of a student and the average GPA of his or her roommates is about .The answers (in
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 a college student’s major and his or her starting salary after graduation.”(b) “We found a high correlation (r = 1.09) between
What are the units? Your data consist of observations on the weight gain over a four-week period of several subjects (measured in pounds) and the food intake of these subjects (measured in calories). In what units are each of the following descriptive statistics measured?(a) The mean food intake of
Body mass and metabolic rate. The body mass data in Table 14.1 are given in pounds. There are 2.2 pounds in a kilogram. If we changed the data from pounds to kilograms, how would the mean body mass change? How would the correlation between body mass and metabolic rate change?306 CHAPTER 14
Strong association but no correlation. The gas mileage of an automobile first increases and then decreases as the speed increases. Suppose that this relationship is very regular, as shown by the following data on speed (miles per hour) and mileage (miles per gallon):Speed: 30 40 50 60 70 Mileage:
Who burns more energy? Table 14.1 gives data on the lean body mass and metabolic rate for 12 women and 7 men. You made a scatterplot of these data in Exercise 14.14.(a) Do you think the correlation will be about the same for men and women or quite different for the two groups? Why?(b) Calculate r
The professor swims. Exercise 14.13 gives data on the time to swim 2000 yards and the pulse rate after swimming for a middle-aged professor.(a) Use a calculator to find the correlation r. Explain from looking at the scatterplot why this value of r is reasonable.(b) Suppose that the times had been
Stretching a scatterplot. Changing the units of measurement can greatly alter the appearance of a scatterplot. Return to the fossil data from Example 3:Femur: 38 56 59 64 74 Humerus: 41 63 70 72 84 Chapter 14 Exercises 305 These measurements are in centimeters. Suppose a deranged scientist measured
Marriage. Suppose that men always married women 4 years younger than themselves. Draw a scatterplot of the ages of 6 married couples, with the husband’s age as the explanatory variable. What is the correlation r for your data? Why?
Who burns more energy? Metabolic rate, the rate at which the body consumes energy, is important in studies of weight gain, dieting, and exercise.Table 14.1 gives data on the lean body mass and resting metabolic rate for 12 women and 7 men who are subjects in a study of dieting. Lean body mass,
The professor swims. Professor Moore swims 2000 yards regularly in a vain attempt to undo middle age. Here are his times (in minutes) and his pulse rate (in beats per minute) after swimming for 23 sessions in the pool:Time: 34.12 35.72 34.72 34.05 34.13 35.72 36.17 35.57 Pulse: 152 124 140 152 146
Outliers and correlation. Figure 14.10 contains outliers marked A, B, and C. In Figure 14.11 the point marked A is an outlier. Removing the outliers will increase the correlation r in one figure and decrease r in the other figure.What happens in each figure, and why?
Calories and salt in hot dogs. Is the correlation r for the data in Figure 14.11 near −1, clearly negative but not near −1, near 0, clearly positive but not near 1, or near 1? Explain your answer.
IQ and GPA. Is the correlation r for the data in Figure 14.10 near −1, clearly negative but not near −1, near 0, clearly positive but not near 1, or near 1? Explain your answer.
Calories and salt in hot dogs. Figure 14.11 shows the calories and sodium content in 17 brands of meat hot dogs. Describe the overall pattern of these data. In what way is the point marked A unusual?
Living on campus. A February 2, 2008, article in the Columbus Dispatch reported a study on the distances students lived from campus and 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 short drive 3.12 Within the

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