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Introduction To The Practice Of Statistics 6th Edition David S. Moore, George P. McCabe, Bruce A. Craig - Solutions
Fuel consumption and speed. Exercise 2.22(page 99) gives data on the fuel consumption y of a car at various speeds x. The relationship is strongly curved: fuel used decreases with increasing speed at low speeds, then increases again as higher speeds are reached. The equation of the least-squares
Average monthly temperatures. Here are the average monthly temperatures for Chicago, Illinois:Month 1 2 3 4 5 6 Temperature (◦F) 21.0 25.4 37.2 48.6 58.9 68.6 Month 7 8 9 10 11 12 Temperature (◦F) 73.2 71.7 64.4 52.8 40.0 26.6 In this table, months are coded as integers, with January
Price and ounces. In Example 2.2 (page 84)and Exercise 2.3 (page 85) we examined the relationship between the price and the size of a Mocha Frappuccinoc . The 12-ounce Tall drink costs $3.15, the 16-ounce Grande is $3.65, and the 24-ounce Venti is $4.15.(a) Plot the data and describe the
Find the sum of the residuals. Here are the 16 residuals for the NEA data rounded to two decimal places:0.37 −0.70 0.10 −0.34 0.19 0.61 −0.26 −0.98 1.64 −0.18 −0.23 0.54 −0.54 −1.11 0.93 −0.03 Find the sum of these residuals. Note that the sum is not exactly zero because of
Find the predicted value and the residual. Another individual in the NEA data set has NEA increase equal to 143 calories and fat gain equal to 3.2 kg. Find the predicted value of fat gain for this individual and then calculate the residual. Explain why this residual is negative.
CHALLENGE The decay product is toxic. Unfortunately, the main product of the decay of the pesticide fenthion is fenthion sulfoxide, which is also toxic.Here are data on the total concentration of fenthion and fenthion sulfoxide in the same specimens of olive oil described in the previous
CH ALLENGE Pesticide decay. Fenthion is a pesticide used to control the olive fruit fly. There are government limits on the amount of pesticide residue that can be present in olive products.Because the pesticide decays over time, producers of olive oil might simply store the oil until the fenthion
CH ALLENGE Class attendance and grades. A study of class attendance and grades among first-year students at a state university showed that in general students who attended a higher percent of their classes earned higher grades. Class attendance explained 16% of the variation in grade index among
Predict final-exam scores. In Professor Friedman’s economics course the correlation between the students’ total scores before the final examination and their final-examination scores is r = 0.55. The pre-exam totals for all students in the course have mean 270 and standard deviation 30. The
Icicle growth. The data for Run 8903 in Table 2.4(page 100) describe how the length y in centimeters of an icicle increases over time x. Time is measured in minutes.(a) What are the numerical values and units of measurement for each of x, sx, y, sy, and the correlation r between x and y?(b) There
CHALLENGE A property of the least-squares regression line. Use the equation for the least- squares regression line to show that this line always passes through the point (x, y).
Heights of husbands and wives. The mean height of American women in their early twenties is about 64.5 inches and the standard deviation is about 2.5 inches. The mean height of men the same age is about 68.5 inches, with standard deviation about 2.7 inches. If the correlation between the heights of
IQ and self-concept. Table 1.9 (page 29) reports data on 78 seventh-grade students.We want to know how well each of IQ score and self-concept score predicts GPA using least-squares regression.We also want to know which of these explanatory variables predicts GPA better. Give numerical measures that
Metabolic rate and lean body mass. Compute the mean and the standard deviation of the metabolic rates and lean body masses in Exercise 2.21 (page 98) and the correlation between these two variables.Use these values to find the slope of the regression line of metabolic rate on lean body mass. Also
Icicle growth. Find the mean and standard deviation of the times and icicle lengths for the data on Run 8903 in Table 2.4 (page 100). Find the correlation between the two variables. Use these five numbers to find the equation of the regression line for predicting length from time. Verify that your
Stocks and Treasury bills. The scatterplot in Figure 2.7 (page 96) suggests that returns on common stocks may be somewhat lower in years with high interest rates. Here is part of the output from software for the regression of stock returns on the Treasury bill returns for the same years:Stock =
Mutual funds. Exercise 2.28 (page 101) gives the returns of 23 Fidelity “sector funds” for the years 2002 and 2003. These mutual funds invest in narrow segments of the stock market. They often rise faster than the overall market in up-years, such as 2003, and fall faster than the market in
Growth of icicles. Table 2.4 (page 100) gives data on the growth of icicles at two rates of water flow.You examined these data in Exercise 2.24. Use leastsquares regression to estimate the rate (centimeters per minute) at which icicles grow at these two flow rates. How does flow rate affect growth?
Problems with feet. Your scatterplot in Exercise 2.20 (page 98) suggests that the severity of the mild foot deformity called MA can help predict the severity of the more serious deformity called HAV.Table 2.2 (page 98) gives data for 38 young patients.(a) Find the equation of the least-squares
Social exclusion and pain. Exercise 2.17 (page 97) gives data from a study that shows that social exclusion causes “real pain.” That is, activity in the area of the brain that responds to physical pain goes up as distress from social exclusion goes up. Your scatterplot in Exercise 2.17 shows a
The Trans-Alaska Oil Pipeline. Figure 2.3 (page 90)plots field measurements on the depth of 100 small defects in the Trans-Alaska Oil Pipeline against laboratory measurements of the same defects.Drawing the y = x line on the graph shows that field measurements tend to be too low for larger defect
Progress in math scores. Every few years, the National Assessment of Educational Progress asks a national sample of eighth-graders to perform the same math tasks. The goal is to get an honest picture of progress in math. Here are the last few national mean scores, on a scale of 0 to 500:25 Year
CAUTION! Perch and bass. Example 2.8 (page 91) gives data from an experiment in ecology.Figure 2.4 is the scatterplot of proportion of perch eaten by bass against the number of perch in a pen before the bass were let in. There is a roughly linear pattern. The least-squares line for predicting
Water discharged by the Mississippi River. Figure 1.10(b) (page 19) is a time plot of the volume of water discharged by the Mississippi River for the years 1954 to 2001. Water volume is recorded in cubic kilometers. The trend line on the plot is the least-squares regression line. The equation of
Revenue and value of NBA teams. Table 2.1 (page 98) gives the values of the 29 teams in the National Basketball Association, along with their operating incomes and revenues. Plots and correlations show that revenue predicts team value much better than does operating income. The least-squares
The effect of a different point. Examine the data in Exercise 2.31 and add a ninth student who has low scores on the second test and the final exam, and fits the overall pattern of the other scores in the data set. Recalculate the least-squares regression line with this additional case and
The effect of an outlier. Refer to the previous exercise. Add a ninth student whose scores on the second test and final exam would lead you to classify the additional data point as an outlier.Recalculate the least-squares regression line with this additional case and summarize the effect it has on
Second test and final exam. Refer to the previous exercise. Here are the data for the second test and the final exam for the same students:Second-test score 158 162 144 162 136 158 175 153 Final-exam score 145 140 145 170 145 175 170 160(a) Plot the data with the second-test scores on the x axis
First test and final exam. In Exercise 2.6 you looked at the relationship between the score on the first test and the score on the final exam in an elementary statistics course. Here are data for eight students from such a course:First-test score 153 144 162 149 127 118 158 153 Final-exam score 145
The regression equation. The equation of a leastsquares regression line is y = 10 + 5x.(a) What is the value of y for x = 5?(b) If x increases by one unit, what is the corresponding increase in y?(c) What is the intercept for this equation?
What fraction of the variation is explained? Consider the following correlations: −0.9, −0.5, −0.3, 0, 0.3, 0.5, and 0.9. For each, give the fraction of the variation in y that is explained by the least-squares regression of y on x. Summarize what you have found from performing these
Would you use the regression equation to predict? Consider the following values for NEA increase: −400, 200, 500, 1000. For each, decide whether you would use the regression equation in Example 2.13 to predict fat gain or whether you would be concerned that the prediction would not be trustworthy
Predict the fat gain. Use the regression equation in Example 2.13 to predict the fat gain for a person whose NEA increases by 600 calories.
Plot the data with the line. Make a sketch of the data in Example 2.12 and plot the line fat gain = 4.505 − (0.00344 × NEA increase)on your sketch. Explain why this line does not give a good fit to the data.
CHALLENGE Effect of a change in units. Consider again the correlation r between the speed of a car and its gas consumption, from the data in Exercise 2.22 (page 99).(a) Transform the data so that speed is measured in miles per hour and fuel consumption in gallons per mile. (There are 1.609
CHALLENGE IQ and GPA. Table 1.9 (page 29) reports data on 78 seventh-grade students. We expect a positive association between IQ and GPA. Moreover, some people think that self-concept is related to school performance. Examine in detail the relationships between GPA and the two explanatory variables
What’s wrong? Each of the following statements contains a blunder. Explain in each case what is wrong.(a) “There is a high correlation between the gender of American workers and their income.”(b) “We found a high correlation (r = 1.09) between students’ ratings of faculty teaching and
Student ratings of teachers. A college newspaper interviews a psychologist about student ratings of the teaching of faculty members. The psychologist says, “The evidence indicates that the correlation between the research productivity and teaching rating of faculty members is close to zero.”
CHALLENGE High correlation does not mean that the values are the same. Investment reports often include correlations. Following a table of correlations among mutual funds, a report adds, “Two funds can have perfect correlation, yet different levels of risk. For example, Fund A and Fund B may be
What is the correlation? Suppose that women always married men 2 years older than themselves.Draw a scatterplot of the ages of 5 married couples, with the wife’s age as the explanatory variable. What is the correlation r for your data? Why?
APPLET CAUTION! Use the applet. Go to the Correlation and Regression applet. Click on the scatterplot to create a group of 10 points in the lower-left corner of the scatterplot with a strong straight-line negative pattern (correlation about−0.9).(a) Add one point at the upper left that is in line
City and highway gas mileage. Table 1.10 (page 31) gives the city and highway gas mileages for 21 two-seater cars, including the Honda Insight gas-electric hybrid car.(a) Make a scatterplot of highway mileage y against city mileage x for all 21 cars. There is a strong positive linear association.
Gas mileage and speed. Exercise 2.22 (page 99)gives data on gas mileage against speed for a small car. Make a scatterplot if you have not already done so, then find the correlation r. Explain why r is close to zero despite a strong relationship between speed and gas used.
APPLET CAUTION! Use the applet. You are going to use the Correlation and Regression applet to make different scatterplots with 10 points that have correlation close to 0.8. Many patterns can have the same correlation. Always plot your data before you trust a correlation.(a) Stop after adding the
An interesting set of data. Make a scatterplot of the following data.x 1 2 3 4 10 10 y 1 3 3 5 1 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
Heights of people who date each other. A student wonders if tall women tend to date taller men than do short women. She measures herself, her dormitory roommate, and the women in the adjoining rooms;then she measures the next man each woman dates.Here are the data (heights in inches):Women (x) 66
Correlations measure strong and weak linear associations. Your scatterplots for Exercises 2.18(page 97) and 2.24 (Table 2.4, page 100) illustrate a quite weak linear association and a very strong linear association. Find the correlations that go with these plots. It isn’t surprising that a
NBA teams. Table 2.1 (page 98) gives the values of the 29 teams in the National Basketball Association, along with their total revenues and operating incomes. You made scatterplots of value against both explanatory variables in Exercise 2.19.(a) Find the correlations of team value with revenue and
Mutual funds. Exercise 2.28 (page 101) gives data on the returns from 23 Fidelity “sector funds” in 2002 (a down-year for stocks) and 2003 (an up-year).(a) Make a scatterplot if you did not do so in Exercise 2.28. Fidelity Gold Fund, the only fund with a positive return in both years, is an
Coffee prices in dollars or euros. Coffee is currently priced in dollars. If it were priced in euros, and the dollar prices in Exercise 2.29 were translated into the equivalent prices in euros, would the correlation between coffee price and percent deforestation change? Explain your answer.
CHALLENGE Mutual funds. Mutual fund reports often give correlations to describe how the prices of different investments are related. You look at the correlations between three Fidelity funds and the Standard & Poor’s 500 stock index, which describes stocks of large U.S. companies. The three funds
IQ and reading scores. Figure 2.6 (page 96) displays the positive association between the IQ scores of fifth-grade students and their reading scores. Do you think the correlation between these variables is closest to r = 0.1, r = 0.6, or r = 0.9? Explain the reason for your guess.
Perch and bass. Figure 2.4 (page 92) displays the positive association between number of prey (perch)present in an area and the proportion eaten by predators (bass).(a) Do you think the correlation between these variables is closest to r = 0.1, r = 0.6, or r = 0.9?Explain the reason for your
The effect of a different point. Examine the data in Exercise 2.31 and add a ninth student who has low scores on the second test and the final exam, and fits the overall pattern of the other scores in the data set. Calculate the correlation and compare it with the correlation that you calculated in
The effect of an outlier. Refer to the previous exercise. Add a ninth student whose scores on the second test and final exam would lead you to classify the additional data point as an outlier.Recalculate the correlation with this additional case and summarize the effect it has on the value of the
Second test and final exam. Refer to the previous exercise. Here are the data for the second test and the final exam for the same students:Second-test score 158 162 144 162 136 158 175 153 Final-exam score 145 140 145 170 145 175 170 160(a) Find the correlation between these two variables.(b) In
First test and final exam. In Exercise 2.6 you looked at the relationship between the score on the first test and the score on the final exam in an elementary statistics course. The data for eight students from such a course are presented in the following table.(a) Find the correlation between
Coffee prices and deforestation. Coffee is a leading export from several developing countries.When coffee prices are high, farmers often clear forest to plant more coffee trees. Here are data for five years on prices paid to coffee growers in Indonesia and the rate of deforestation in a national
CH ALLENGE Mutual funds in another year. The data for 2003 in the previous exercise make sector funds look attractive. Stocks rose sharply in 2003, after falling sharply in 2002 (and also in 2001 and 2000). Let’s look at the percent returns for both 2003 and 2002 for these same 23 funds. Here
Mutual funds. Fidelity Investments, like other large mutual funds companies, offers many “sector funds” that concentrate their investments in narrow segments of the stock market. These funds often rise or fall by much more than the market as a whole.We can group them by broader market sector to
Worms and plant growth. To demonstrate the effect of nematodes (microscopic worms) on plant growth, a botanist introduces different numbers of nematodes into 16 planting pots. He then transplants a tomato seedling into each pot. Here are data on the increase in height of the seedlings (in
Records for men and women in the 10K. Table 2.3 shows the progress of world record times (in seconds) for the 10,000-meter run for both men and women.(a) Make a scatterplot of world record time against year, using separate symbols for men and women.Describe the pattern for each sex. Then compare
CHALLENGE How do icicles grow? How fast do icicles grow? Japanese researchers measured the growth of icicles in a cold chamber under various conditions of temperature, wind, and water flow.16 Table 2.4 contains data produced under two sets of conditions. In both cases, there was no wind and the
World records for the 10K. Table 2.3 shows the progress of world record times (in seconds) for the 10,000-meter run up to mid-2004.15 Concentrate on the women’s world record times. Make a scatterplot with year as the explanatory variable. Describe the pattern of improvement over time that your
Fuel consumption and speed. How does the fuel consumption of a car change as its speed increases? Below are data for a British Ford Escort.Speed is measured in kilometers per hour, and fuel consumption is measured in liters of gasoline used per 100 kilometers traveled.14 Speed Fuel used Speed Fuel
Body mass and metabolic rate. Metabolic rate, the rate at which the body consumes energy, is important in studies of weight gain, dieting, and exercise. The table below 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
Two problems with feet. Metatarsus adductus (call it MA) is a turning in of the front part of the foot that is common in adolescents and usually corrects itself.Hallux abducto valgus (call it HAV) is a deformation of the big toe that is not common in youth and often requires surgery. Perhaps the
Business revenue and team value in the NBA.Management theory says that the value of a business should depend on its operating income, the income produced by the business after taxes. (Operating income excludes income from sales of assets and investments, which don’t reflect the actual
Biological clocks. Many plants and animals have“biological clocks” that coordinate activities with the time of day. When researchers looked at the length of the biological cycles in the plant Arabidopsis by measuring leaf movements, they found that the length of the cycle is not always 24
Social rejection and pain. We often describe our emotional reaction to social rejection as “pain.” A clever study asked whether social rejection causes activity in areas of the brain that are known to be activated by physical pain. If it does, we really do experience social and physical pain in
City and highway gas mileage. Table 1.10 (page 31) gives the city and highway gas mileages for minicompact and two-seater cars. We expect a positive association between the city and highway mileages of a group of vehicles. We have already seen that the Honda Insight is a different type of car, so
Small falcons in Sweden. Often the percent of an animal species in the wild that survive to breed again is lower following a successful breeding season. This is part of nature’s self-regulation, tending to keep population size stable. A study of merlins (small falcons) in northern Sweden observed
Literacy of men and women. Table 1.2 (page 10)shows the percent of men and women at least 15 years old who were literate in 2002 in the major Islamic nations for which data were available. Make a scatterplot of these data, taking male literacy as the explanatory variable. Describe the
Can children estimate their reading ability? The main purpose of the study cited in Exercise 2.11 was to ask whether schoolchildren can estimate their own reading ability. The researchers had the children’s scores on a test of reading ability. They asked each child to estimate his or her reading
Treasury bills and common stocks. What is the relationship between returns from buying Treasury bills and returns from buying common stocks? The stemplots in Figure 1.22 (page 44) show the two individual distributions of percent returns. To see the relationship, we need a scatterplot. Figure 2.7
Reading ability and IQ. A study of reading ability in schoolchildren chose 60 fifth-grade children at random from a school. The researchers had the children’s scores on an IQ test and on a test of reading ability.8 Figure 2.6 (on page 96) plots reading test score (response) against IQ score
Parents’ income and student loans. How well does the income of a college student’s parents predict how much the student will borrow to pay for college? We have data on parents’ income and college debt for a sample of 1200 recent college graduates. What are the explanatory and response
Explanatory and response variables. In each of the following situations, is it more reasonable to simply explore the relationship between the two variables or to view one of the variables as an explanatory variable and the other as a response variable? In the latter case, which is the explanatory
Add an outlier to the plot. Refer to the previous exercise. Add a ninth student whose scores on the second test and final exam would lead you to classify the additional data point as an outlier. Highlight the outlier on your scatterplot and describe the performance of the student on the second exam
Relationship between second test and final exam. Refer to the previous exercise. Here are the data for the second test and the final exam for the same students:Second-test score 158 162 144 162 136 158 175 153 Final-exam score 145 140 145 170 145 175 170 160(a) Explain why you should use the
Relationship between first test and final exam.How strong is the relationship between the score on the first test and the score on the the final exam in an elementary statistics course? Here are data for eight students from such a course:First-test score 153 144 162 149 127 118 158 153 Final-exam
Average temperatures. Here are the average temperatures in degrees for Lafayette, Indiana, during the months of February through May:Month February March April May Temperature (degrees F) 30 41 51 62(a) Explain why month should be the explanatory variable for examining this relationship.(b) Make a
Make a scatterplot. In our Mocha Frappuccino example, the 12-ounce drink costs $3.15, the 16-ounce drink costs $3.65, and the 24-ounce drink costs $4.15. Explain which variable should be used as the explanatory variable and make a scatterplot. Describe the scatterplot and the association between
Replace names by ounces. In the Mocha Frappuccino example, the variable size is categorical, with Tall, Grande, and Venti as the possible values. Suppose you converted these values to the number of ounces: Tall is 12 ounces, Grande is 16 ounces, and Venti is 24 ounces.For studying the relationship
Suppose we used breed size? Suppose that for the dog breed example we were able to obtain some measure of average size for each of the breeds. If we replaced type of dog breed with the average breed size, how would this change the explanation in Example 2.3?
Relationship between first test and final exam. You want to study the relationship between the score on the first test and the score on the final exam for the 35 students enrolled in an elementary statistics class. Who are the individuals for your study?
The Question of Causation
Data Analysis for Two-Way Tables
What are the Cautions about Correlation and Regression
What is Least-Squares Regression
Define Correlation
Explain Scatterplots
SAT mathematics scores and grade point averages. The CSDATA data set described in the Data Appendix contains information on 234 computer science students. We are interested in comparing the SAT Mathematics scores and grade point averages of female students with those of male students. Make two sets
Distribution of income. Each March, the Bureau of Labor Statistics collects detailed information about more than 50,000 randomly selected households. The WORKERS data set contains data on 71,076 people from the March 2002 survey. All of these people were between 25 and 64 years of age and worked
Use software to generate some data. Most statistical software packages have routines for generating values of variables having specified distributions. Use your statistical software to generate 25 observations from the N(20, 5)distribution. Compute the mean and standard deviation x and s of the 25
Returns on stocks. Returns on common stocks are “heavy tailed.” That is, they have more values far from the center in both the low and the high tails than a Normal distribution would have.However, average returns for many individual stocks over longer periods of time become more Normal.(a)
Proportions older than 65. We know that the distribution of the percents of state residents over 65 years of age has a low outlier (Alaska) and a high outlier (Florida). The stemplot in Exercise 1.21(page 24) looks unimodal and roughly symmetric.(a) Sketch what a Normal quantile plot would look
Damage caused by tornados. The average damage caused by tornadoes in the states (Table 1.5, page 25) and the estimated amount of oil recovered from different oil wells (Exercise 1.39, page 28) both have right-skewed distributions.Choose one of these data sets. Make a Normal quantile plot. How is
CHALLENGE Norms for reading scores. Raw scores on behavioral tests are often transformed for easier comparison. A test of reading ability has mean 75 and standard deviation 10 when given to third-graders. Sixth-graders have mean score 82 and standard deviation 11 on the same test.To provide
Barry Bonds. The single-season home run record was broken by Barry Bonds of the San Francisco Giants in 2001, when he hit 73 home runs. Here are Bonds’s home run totals from 1986 (his first year) to 2003:16 25 24 19 33 25 34 46 37 33 42 40 37 34 49 73 46 45 Make a stemplot of these data.
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