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

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 measured length in centimeters, how would the correlation change?(There are 2.54 centimeters in an
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 and brain size (in units of 10,000 pixels) of six individuals are as follows:Brain size: 100 90 95
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 and brain size (in units of 10,000 pixels) of six individuals are as follows:Brain size: 100 90 95
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 and brain size (in units of 10,000 pixels) of six individuals are as follows:Brain size: 100 90 95
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 index. Joe wants to buy a mutual fund that does not track the index closely. He reads that monthly
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 remaining votes. Table II.4 gives the percentage of the popular vote won by President Bush in each
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: See pages 253–255.)
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 on campus). The two high times reflect delays due to an accident and icy roads. Remove these three
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, with the dates in order along the rows:8.25 7.83 8.30 8.42 8.50 8.67 8.17 9.00 9.00 8.17 7.92 9.00
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 2007. Using Table 16.1, make a graph that shows how the price of gold changed in real terms over this
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 calculation to justify your answer.
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 power as$24,000 had in 1981? (Hint: See pages 343–344.)368 Part II Review
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 have the same buying power they had in 1980?
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 line to predict weight after 30 days? (Hint: See pages 313–318.)
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 soap lost weight.(b) Mr. Boggs did not measure the weight of the soap on Day 4. Use the regression
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 but not close to 1, close to 0, negative but not close to −1, or close to −1? Explain your answer.
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 rain forest with body weight 600 kilograms. Predict the brain weight for this species. (Hint: See
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 what the number tells us.
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 312–313.)
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 mouse weight to be positive.(b) The mean tail length turns out to be 9.8 centimeters. What is the
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 length of the tails. (Hint: See page 297.)(b) The first quartile of the tail lengths. (Hint: See page
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. Say as specifically as you can what the correlation r between yearly wine consumption and yearly
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 II Review Exercises 365(a) What is the median SAT score? (Hint: See pages 270–272.)(b) You run a
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 rule to answer these questions.(a) Between what values do the middle 95% of head circumferences
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? Find the mean for the 25 remaining states to verify your answer. (Hint: See page 249.)
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 team.) Make a histogram of these data. Does the distribution have a clear shape: roughly symmetric,
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 roughly symmetric, skewed to the right, or skewed to the left? Which states (if any) are outliers?
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 says about any changes in the CPI.
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 the prices of such things as white bread and gasoline have changed over time. How does the current
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 Web address www.bls.gov/cpi. Under “GET DETAILED STATISTICS: Create Customized Tables (one
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 to “Agencies.”(a) Bureau of Economic Analysis (Department of Commerce).(b) National Center for
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 some possible measures in each of the following categories:(a) Statistics to be compiled from
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 clearly, to someone who knows no statistics, why such cuts reduce the accuracy of the resulting
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, workers at the 33rd percentile experienced a 14 percent drop in the real wage, workers at the 66th
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 poverty. An economist looked at the poverty lines over time and said that they “show a pattern of
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 applies to the region or local area.The BLS says that the local CPIs should be used with caution
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 seasonal variation(i.e., not seasonally adjusted indexes) for escalation.” “Escalation” here
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 Montana.(b) Jim heats his home with a wood stove and does not have air-conditioning.(c) Luis and Maria were 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 22% and 6% come from? Why does the cost of buying get more weight in the index?
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 might not go up at all, even though consumers must pay more. Explain why.
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 Government Statistics The real income that marks off the top 5% of households rose from $143,619 to$174,012
College tuition. Tuition for Colorado residents at Colorado State University has increased as follows (use tuition at your own college if you have those data):Year: 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 Tuition ($): 1008 1275 1474 1636 1855 2022 2174 2258 2340 2502 2908
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 employers reluctant to hire workers with low skills and so increases unemployment. Here is information on
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 faster or slower than consumer prices in general? How do you know?
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 the real cost go down between 1976 and December 2007? The CPI in December 2007 was 210.0.
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 decade?
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 $266,438 that year.How do these amounts compare in real terms?
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 latest value of the CPI (it’s on the BLS Web site, www.bls.gov/cpi/home.htm) and use it to restate
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 per year. They were quite comfortable—that was about the median family income in 1975. How much
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 $50,000 had in 2003?
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 occurred in 2004). The Red Sox victory in 2004 supposedly broke the curse. How much is $125,000 in 2004
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 in 1985 and 2005:1985 1985 2005 2005 Item quantity price quantity price Olive oil 20 pints
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 50 gallons 5.08/gallon 354 CHAPTER 16 The Consumer Price Index and Government Statistics After a
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 2007 was 219.4 in Los Angeles and 229.4 in New York.(a) These numbers tell us that prices rose
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 Price Index (CPI). If the CPI is 120, goods and services that cost $100 in the base period now cost
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 1988, 1,736,461 in 1998, and 1,265,879 in 2005. Give an index number for toxic chemical releases in each
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 was this?(b) By how many points did the gasoline price index number change between 1997 and 2007? What
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 index number 552.9 tells us about the rise in college tuition between the base period and September
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 index numbers (1997 = 100) for 1987, 1997, and 2007.
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 in 2006 dollars. By what percentage did the real earnings of production workers change between 1987
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 Statistics: Concepts and Controversies Web site, www.whfreeman.com/scc7e, and look at the Normal
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 to be in the top 25% of all scores?EXPLORING THE WEB
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 percentile that appears in Table B.)
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 of 12%, with a standard deviation of 16.5%. Take this Normal distribution to be the distribution of
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 Normally distributed with mean 100 and standard deviation 15. When the test was standardized in Japan, the
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
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 senior women’s scores on the SAT Math test followed a Normal distribution with mean 499 and standard
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, the scores of college-bound senior men on the SAT Math test followed a Normal distribution with mean
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 combined
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 2007, the combined scores of the
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 that in fact only 43% of the voters support Floyd. The percentage favoring Floyd in a random sample of
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 25 to March 1, 2008. If we took many SRSs of size 3500 (the sample size used by the Gallup Poll),
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 aged 18 to 24 is approximately Normal? Explain your answer.
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 standard deviation 2.5 inches. What percentage of women are taller than a man of average(mean) height?
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 questions.(a) What percentage of men are taller than 77.5 inches?(b) Between what heights do the middle
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 deviation are correctly located. (Hint: Draw the curve first, locate the points where the curvature changes,
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 and
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
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 the 68–95–99.7 rule to answer the following questions.(a) Almost all (99.7%) pregnancies fall in
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 among these points. For each curve, which point is the median and which is the mean?AppendixLO1
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 feet)?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. Between which heights do the middle 95%of men fall?AppendixLO1
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 discussed in this chapter. From either of these documents, give one issue that is discussed in the
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 Manual for the Use of Human Subjects in Research (see the links along the left side of the page) to
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 either the health and biological sciences or the social and behavioral sciences link. Next, select the
Web-based exercise. The Journal of Medical Internet Research contains an article on ethical issues that arise in providing online psychotherapeutic interventions. Visit theWeb page,www.jmir.org/2000/1/e5/, and read the article. Describe at least two of the ethical issues discussed in the

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