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business
business statistics

Questions and Answers of Business Statistics

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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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.
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
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
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
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.
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
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
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
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
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
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
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
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
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
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
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
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?
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
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
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
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
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
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
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
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?
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
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,
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
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
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
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
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
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.
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
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
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)
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
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).
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
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
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
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
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
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
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
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
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
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.

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