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business statistics

Questions and Answers of Business Statistics

Measuring snakes. For a biology project, you measure the length (inches)and weight (grams) of 12 snakes.(a) Explain why you expect the correlation between length and weight to be positive.(b) If you
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?
Brain size and intelligence. For centuries people have associated intelligence with brain size. A recent study used magnetic resonance imaging to measure the brain size of several individuals.The IQ
Brain size and intelligence. For centuries people have associated intelligence with brain size. A recent study used magnetic resonance imaging to measure the brain size of several individuals.The IQ
Brain size and intelligence. For centuries people have associated intelligence with brain size. A recent study used magnetic resonance imaging to measure the brain size of several individuals.The IQ
Statistics for investing. Joe’s retirement plan invests in stocks through an “index fund” that follows the behavior of the stock market as a whole, as measured by the Standard & Poor’s 500
The 2004 election. George Bush was reelected president in 2004 with 51.0% of the popular vote. His Democratic opponent, John Kerry, received 48.1%of the vote, with minor candidates taking the
House prices. An August 26, 2007, article in the New York Times reported that the median housing price was about $220,000.Would the mean selling price be higher, about the same, or lower? Why?(Hint:
Drive time outliers. In the previous exercise, there are three outliers in Professor Moore’s drive times to work. All three can be explained. The low time is the day after Thanksgiving (no traffic
Drive time. Professor Moore, who lives a few miles outside a college town, records the time he takes to drive to the college each morning. Here are the times (in minutes) for 42 consecutive weekdays,
The price of gold. Some people recommend that investors buy gold “to protect against inflation.” Here are the prices of an ounce of gold at the end of the year for the years between 1985 and
Affording a Steinway. A Steinway concert grand piano cost $13,500 in 1976. A similar Steinway cost $139,500 in 2007. Has the cost of the piano gone up or down in real terms? Using Table 16.1, give a
Affording a Mercedes. A Mercedes-Benz 190 cost $24,000 in 1981, when the CPI (1982–84 = 100) was 90.9. The average CPI for 2007 was 207.3.How many 2007 dollars must you earn to have the same buying
Keeping up with the Joneses. The Jones family had a household income of $30,000 in 1980, when the CPI (1982–84 = 100) was 82.4. The CPI for 2007 was 207.3. How much must the Joneses earn in 2007 to
Prediction? Use the regression equation in the previous exercise to predict the weight of the soap after 30 days. Why is it clear that your answer makes no sense? What’s wrong with using the
Regression. The equation for the least-squares regression line for the data in Table II.3 is weight = 133.2 − 6.31 × day(a) Explain carefully what the slope b= −6.31 tells us about how fast the
Scatterplot. Plot the weight of the bar of soap against day. Is the overall pattern roughly straight-line? Based on your scatterplot, is the correlation between day and weight close to 1, positive
Prediction. The line on the scatterplot in Figure II.3 is the leastsquares regression line for predicting brain weight from body weight. Suppose that a new mammal species is discovered hidden in the
Brain and body. The correlation between body weight and brain weight is r = 0.86. How well does body weight explain brain weight for mammals?Give a number to answer this question, and briefly explain
Dolphins and hippos. One reaction to this scatterplot is “Dolphins are smart, hippos are dumb.” What feature of the plot lies behind this reaction?
Dolphins and hippos. The points for the dolphin and hippopotamus are labeled in Figure II.3. Read from the graph the approximate body weight and brain weight for these two species. (Hint: See pages
More data on mice. For a biology project, you measure the tail length(centimeters) and weight (grams) of 12 mice of the same variety.(a) Explain why you expect the correlation between tail length and
Data on mice. For a biology project, you measure the tail length (centimeters)and weight (grams) of 12 mice of the same variety. What units of measurement do each of the following have?(a) The mean
Explaining correlation. You have data on the yearly wine consumption(liters of alcohol from drinking wine per person) and yearly deaths from cirrhosis of the liver for several developed countries.
SAT scores. The scale for SAT exam scores is set so that the distribution of scores is approximately Normal with mean 500 and standard deviation 100.Answer these questions without using a table.Part
Big heads? The army reports that the distribution of head circumference among male soldiers is approximately Normal with mean 22.8 inches and standard deviation 1.1 inches. Use the 68–95–99.7
Poverty in the states. Find the mean percentage of state residents living in poverty from the data in Table II.1. If we removed Mississippi from the data, would the mean increase or decrease? Why?
Quarterbacks. Give the five-number summary for the data on passing yards for NFL quarterbacks from Table II.2.
Poverty in the states. Give the five-number summary for the data on poverty from Table II.1. (Hint: See page 244.)
Quarterbacks. Table II.2 gives the total passing yards for National Football League starting quarterbacks during the 2007 season. (These are the quarterbacks with the most passing attempts on each
Poverty in the states. Table II.1 gives the percentages of people living below the poverty line in the 26 states east of the Mississippi River. Make a stemplot of these data. Is the distribution
Web-based exercise. Search the Internet to find a recent news report on the CPI. For example, a Google search of“latest CPI” turned up a couple of articles. Summarize what the article you choose
Web-based exercise. If you like data, you can go to the BLS data page, www.bls.gov/cpi/home.htm, and under “Get Detailed CPI Statistics”choose “Average Price Data,” and see for yourself how
Web-based exercise. Go to the Bureau of Labor Statistics Web site and find the most recent index number for the cost of college tuition.You can find this by conducting a public-data query. Go to the
Statistical agencies. Write a short description of the work of one of these government statistical agencies. You can find information by starting at the FedStats Web site (www.fedstats.gov) and going
Measuring the effects of crime. We wish to include, as part of a set of social statistics, measures of the amount of crime and of the impact of crime on people’s attitudes and activities. Suggest
The General Social Survey. The General Social Survey places much emphasis on asking many of the same questions year after year. Why do you think it does this?
Saving money? One way to cut the cost of government statistics is to reduce the sizes of the samples.We might, for example, cut the Current Population Survey from 50,000 households to 20,000. Explain
Real wages (optional). In one of the many reports on stagnant incomes in the United States, we read this: “Practically every income group faced a decline in real wages during the 1980s. However,
The poverty line. The federal government announces “poverty lines”each year for households of different sizes. Households with income below the announced levels are considered to be living in
More CPIs. In addition to the national CPI, the BLS publishes CPIs for 4 regions and for 37 local areas. Each regional and local CPI is based on just the part of the national sample of prices that
Seasonal adjustment. Like many government data series, the CPI is published in both unadjusted and seasonally adjusted forms. The BLS says that it “strongly recommends using indexes unadjusted for
The CPI doesn’t fit me. The CPI may not measure your personal experience with changing prices. Explain why the CPI will not fit each of these people:(a) Marcia lives on a cattle ranch in
Item weights in the CPI. The cost of buying a house (with the investment component removed) makes up about 22% of the CPI. The cost of renting a place to live makes up about 6%. Where do the weights
Cable TV. Suppose that cable television systems across the country add channels to their lineup and raise the monthly fee they charge subscribers. The part of the CPI that tracks cable TV prices
Rising incomes? In Example 4, we see that the median real income (in 2006 dollars) of all households rose from $46,249 in 1987 to $48,201 in 2006.356 CHAPTER 16 The Consumer Price Index and
College tuition. Tuition for Colorado residents at Colorado State University has increased as follows (use tuition at your own college if you have those data):Year: 1983 1985 1987 1989 1991 1993 1995
The minimum wage. The federal government sets the minimum hourly wage that employers can pay a worker. Labor wants a high minimum wage, but many economists argue that too high a minimum makes
Paying for Harvard. Harvard charged $5900 for tuition, room, and board in 1976. The 2007 charge was $42,078. Express Harvard’s 1976 charges in 2007 dollars. Did the cost of going to Harvard go up
Calling London. A 10-minute telephone call to London via AT&T cost$12 in 1976 and $14 in December 2007 using an occasional calling plan. Compare the real costs of these calls. By what percentage did
Joe DiMaggio. Yankee center fielder Joe DiMaggio was paid $32,000 in 1940 and $100,000 in 1950. Express his 1940 salary in 1950 dollars. By what percentage did DiMaggio’s real income change in the
Good golfers. In 2007, Tiger Woods won $10,867,052 on the Professional Golfers Association tour. The leading money winner in 1940 was Ben Hogan, at $10,655. Jack Nicklaus, the leader in 1976, won
Microwaves on sale. The prices of new gadgets often start high and then fall rapidly. The first home microwave oven cost $1300 in 1955. You can now buy a better microwave oven for $100. Find the
Living too long? If both husband and wife are alive at age 65, in half the cases at least one will still be alive at age 93, 28 years later. Myrna and Bill retired in 1975 with an income of $12,000
Dream on. When Julie started college in 2003, she set a goal of making$50,000 when she graduated. Julie graduated in 2007. What must Julie earn in 2007 in order to have the same buying power that
The curse of the Bambino. In 1920 the Boston Red Sox sold Babe Ruth to the New York Yankees for $125,000. Between 1920 and 2004, the Yankees won 26 World Series and the Red Sox won 1 (and that
The Guru Price Index. A guru purchases only olive oil, loincloths, and copies of the Atharva Veda, from which he selects mantras for his disciples.Here are the quantities and prices of his purchases
The Food Faddist Price Index. A food faddist eats only steak, rice, and ice cream. In 1995, he bought:Item 1995 quantity 1995 price Steak 200 pounds $5.45/pound Rice 300 pounds 0.49/pound Ice cream
Los Angeles and New York. The Bureau of Labor Statistics publishes separate consumer price indexes for major metropolitan areas in addition to the national CPI. The CPI (1982–84 = 100) in December
How much can a dollar buy? The buying power of a dollar changes over time. The Bureau of Labor Statistics measures the cost of a “market basket” of goods and services to compile its Consumer
Toxic releases. The Environmental Protection Agency requires industry to report releases of any of a list of toxic chemicals. The total amounts released(in thousands of pounds) were 3,006,577 in
The price of gasoline. Use your results from Exercise 16.3 to answer these questions.(a) By how many points did the gasoline price index number change between 1987 and 2007? What percentage change
The cost of college. The part of the CPI that measures the cost of college tuition (1982–84 = 100) was 552.9 in September 2007. The overall CPI was 208.5 that month.(a) Explain exactly what the
The price of gasoline. The yearly average price of unleaded regular gasoline has fluctuated as follows:1987: $0.95 per gallon 1997: $1.23 per gallon 2007: $2.80 per gallon Give the gasoline price
Production workers. Let’s look at production workers, the traditional “working men” (and women). Their average hourly earnings were $9.14 in 1987 and $16.76 in 2006. Compute the 1987 earnings
Baseball salaries. Refer to Example 3. Convert the 1987 median baseball salary into 2007 dollars.
Web-based exercise. If you did any of Exercises 13.21 to 13.30, check your calculations using the Normal Curve applet described in the previous exercise.
Web-based exercise. Tables of areas under a Normal curve, like Table B at the back of this book, are still common but are also giving way to “applets” that let you find areas visually. Go to the
High IQ scores. Scores on theWechsler 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
Young women’s heights. The heights of women aged 18 to 24 are approximately Normal with mean 65 inches and standard deviation 2.5 inches.How tall are the tallest 10% of women? (Use the closest
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?
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
Japanese IQ scores. The Wechsler Intelligence Scale for Children is used (in several languages) in the United States and Europe. Scores in each Chapter 13 Exercises 285 case are approximately
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
Women’s SAT scores. The average performance of women on the SAT, especially the math part, is lower than that of men. The reasons for this gender gap are controversial. In 2007, college-bound
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 2007,
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
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
Am I winning? Congressman Floyd commissions a sample survey of voters to learn what percentage favor him in his race for reelection. To avoid spending too much, he samples only 50 voters. Suppose
Sampling. Suppose that the proportion of all adult Americans who rate economic conditions in the United States as poor is p = 0.37.This number is consistent with a Gallup Poll conducted from February
Heights of young adults. The mean height of men aged 18 to 24 is about 70 inches. Women that age have a mean height of about 65 inches. Do you think that the distribution of heights for all Americans
Heights of men and women. The heights of young women are approximately Normal with mean 65 inches and standard deviation 2.5 inches. The heights of men in the same age group have mean 70 inches and
More on men’s heights. The distribution of heights of young men is approximately Normal with mean 70 inches and standard deviation 2.5 inches.Use the 68–95–99.7 rule to answer the following
Men’s heights. The distribution of heights of young men is approximately Normal with mean 70 inches and standard deviation 2.5 inches. Sketch a Normal curve on which this mean and standard
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
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
A Normal curve. What are the mean and standard deviation of the Normal curve in Figure 13.14?
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
What percentage of all students have IQ scores 144 or higher? None of the 74 students in our sample school had scores this high. Are you surprised at this? Why?
What percentage of IQ scores for rural Midwest seventh-graders are less than 100?
Between what values do the IQ scores of 95% of all rural Midwest seventhgraders lie?
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
Density curves.(a) Sketch a density curve that is symmetric but has a shape different from that of the Normal curves.(b) Sketch a density curve that is strongly skewed to the right.AppendixLO1
SAT scores. How high must a student score on the SAT Mathematics test to fall in the top 20% of all scores?AppendixLO1
Heights of young men. The distribution of heights of young men is approximately Normal with mean 70 inches and standard deviation 2.5 inches. What is the standard score of a height of 72 inches (6
Heights of young men. The distribution of heights of young men is approximately Normal with mean 70 inches and standard deviation 2.5 inches. Between which heights do the middle 95%of men
Web-based exercise. The official ethical codes of the American Statistical Association and the American Psychological Association are long documents that address many issues in addition to those
Web-based exercise. For a glimpse at the work of an institutional review board, visit the site of the University of Pittsburgh’s board, www.irb.pitt.edu/manual/default.htm. Look at the Reference
Web-based exercise. The University of Minnesota has aWeb page intended to educate readers about informed consent. The Web address is www.research.umn.edu/consent/. Visit the Web page and select
Web-based exercise. The Journal of Medical Internet Research contains an article on ethical issues that arise in providing online psychotherapeutic interventions. Visit theWeb

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