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a course in statistics with r
Mind On Statistics 5th Edition Jessica M Utts, Robert F Heckard - Solutions
3.55 Refer back to Exercise 3.7 about stopping distance and vehicle speed. The least squares line for these data is Average distance 5 244.2 1 5.7 (Speed)a. Use this equation to estimate the average stopping distance when the speed is 80 miles per hour. Do you think this is an accurate estimate?
3.54 Sketch a scatterplot in which the correlation without an outlier is negative, but the correlation when the outlier is added is positive. Indicate on your plot which point is the outlier.General Section Exercises
3.53 Sketch a scatterplot in which the presence of an outlier decreases the observed correlation between the response and explanatory variables. Indicate on your plot which point is the outlier.
3.52 The physical dataset on the companion website gives heights (inches) and head circumferences (cm) for a sample of college students. For females only, the correlation between the two variables is 0.05, while for males only, the correlation is 0.19. For the combined sample of males and females,
3.51 An article in the Sacramento Bee (May 29, 1998, p. A17)noted, “Americans are just too fat, researchers say, with 54 percent of all adults heavier than is healthy. If the trend continues, experts say that within a few generations virtually every U.S. adult will be overweight.” This
3.50 The average January temperatures (y) and geographic latitudes(x) of 20 cities in the United States were given in the table for Exercise 3.9. The regression equation for these data was given in Exercise 3.24 as y^ 5 126 2 2.34x. The value of r2 for this relationship is 73.3%. What is the
3.49 Suppose you know that the slope of a regression line is b1 5 13.5. Based on this value, explain what you know and do not know about the strength and direction of the relationship between the two variables.
3.48 The data in the table for Exercise 3.12 show the heights and average of parents’ heights, called “mid-parent height,” for each of 18 college students. The data are also in the file UCDchap3 where the mother’s and father’s heights are provided for each student as well. Student’s
3.47 In a regression analysis, the total sum of squares (SSTO) is 800, and the error sum of squares (SSE) is 200. What is the value for r 2?
3.46 Refer to Exercise 3.12 and the table for Exercise 3.12 in which heights and mid-parent heights are given for 18 college students (Data source: UCDchap3 dataset on the website for this book). Draw a scatterplot for the data, using different symbols for males and females as instructed in part(b)
3.44 The correlation between latitude and average August temperature (in degrees Fahrenheit) is 20.78 for the 20 cities shown in the table for Exercise 3.9. (The data also are in the dataset temperature on the companion website.)a. Calculate r 2 and write a sentence that interprets it in the
3.43 The correlation between height and weight is r 5 0.40 for 12th-grade male respondents (n 5 1501) in a survey done in 2003 by the U.S. Centers for Disease Control and Prevention as part of the Youth Risk Behavior Surveillance System. (The raw data are in the dataset YouthRisk03 on the companion
3.42 For each pair of variables, identify whether the pair is likely to have a positive correlation, a negative correlation, or no correlation. Briefly indicate your reasoning.a. Verbal skills and age for children under 12 years old.b. Height of husband and height of wife.c. Number of dogs and
3.41 For each pair of variables, identify whether the pair is likely to have a positive correlation, a negative correlation, or no correlation. Briefly indicate your reasoning.a. Hours of television watched per day and grade point average for college students.b. Number of liquor stores and number
3.40 The dataset bodytemp on the companion website gives age in years and body temperature in degrees Fahrenheit for 100 blood donors ranging in age from 17 to 84 years old.A scatterplot showed a linear relationship with a correlation between age and body temperature of 20.313. Using this value,
3.39 In the 1996 General Social Survey, the correlation between respondent age and hours of daily television viewing for n 5 1913 respondents was r 5 10.12. Using this value, characterize the nature of the relationship between age and hours of television watching in 1996.
3.38 Refer to the figure for the previous exercises. In scrambled order, correlation values for these four graphs are 20.9, 0, 10.3, and 10.6. Match these correlation values to the graphs.
3.37 The figure for this exercise (below) shows four graphs. Assume that all four graphs have the same numerical scales for the two axes. Which graph shows the strongest relationship between the two variables? Which graph shows the weakest?Graph 1 Graph 2 Graph 3 Graph 4
3.36 Sketch a scatterplot showing data for which the correlation is r 5 21.
3.35 Suppose two variables have a deterministic linear relationship with a positive association. What is the value of the correlation between them?
3.34 Explain how two variables can have a perfect curved relationship yet have zero correlation. Draw a picture of a set of data meeting those criteria.
3.33 In Figure 3.11 (p. 84), we observed that the correlation between the left and right handspans of college students was 0.95. The handspans were measured in centimeters. What would be the correlation if the handspans were converted to inches? Explain.General Section Exercises
3.32 Which implies a stronger linear relationship: a correlation of 10.4 or a correlation of 20.6? Briefly explain.
3.31 For 19 female bears, the correlation between x 5 length of the bear (inches) and y 5 chest girth (inches) is r 5 0.82. (Data source: bears-female dataset on the companion website.)a. Describe how chest girth will change when length is increased.b. Assuming that there are no outliers and the
3.30 Suppose the value of r2 is 100% for the relationship between two variables.a. What is indicated about the strength of the relationship?b. What are the two possible values for the correlation coefficient for the two variables?
3.29 For n 5 188 students, the correlation between y 5 fastest speed ever driven and x 5 number randomly picked between 1 and 10 is about r 5 0. Describe what this cor relation indicates about the association between the fastest speed driven and picking a number between 1 and 10.
3.28 Remember that r 2 can be expressed as a proportion or as a percent. (When written as a percent, the percent sign will always be included.)a. Explain which of the following could not be a value for r 2: 0, 20.25, 0.3, 1.0, 1.7, 25%, 250%, 1200%.b. Refer to the values in part (a). Which one of
3.27 Which of the numbers 0, 0.25, 21.7, 20.5, and 2.5 could not be values of a correlation coefficient? In each case, explain why.
3.26 The least squares regression equation for the data in the following table is y^ 5 5 1 2x.x 4 4 7 10 10 y 15 11 19 21 29a. Calculate the value of y^ for each data point.b. Calculate the sum of squared errors for this situation.Section 3.3 Skillbuilder Exercises
3.25 The data for this exercise are as follows:x 1 2 3 4 y 4 10 14 16a. Determine the sum of squared errors (SSE) for each of the following two lines:Line 1: y^ 5 3 1 3x Line 2: y^ 5 1 1 4xb. By the least squares criterion, which of the two lines in part (a) is better for these data? Why is it
3.24 The average January temperatures (y) and geographic latitudes (x) of 20 cities in the United States were given in the table for Exercise 3.9. (The data are part of the temperature dataset on the companion website.) The regression equation for these data is y^ 5 126 2 2.34xa. What is the slope
3.23 Refer to Exercise 3.22.a. Predict the pulse rate after marching for somebody with a resting pulse rate of 70.b. Suppose the pulse rate after marching is 76 for somebody whose resting pulse rate is 70. What is the residual (prediction error) for this individual?
3.22 The figure for Exercise 3.8 is a scatterplot of pulse rate after marching in place for 1 minute (y) versus resting pulse rate measured before marching (x) for n 5 63 individuals.(The data are in the pulsemarch dataset on the companion website.) The regression equation for these data is Pulse
3.21 Iman (1994) reports that for professional golfers, a re gression equation relating x 5 putting distance (in feet) and y 5 success rate (in percent) based on observations of distances ranging from 5 feet to 15 feet is Success rate 5 76.5 2 3.95 (Distance)a. What percentage of success would you
3.20 Imagine a regression line that relates y 5 average systolic blood pressure to x 5 age. The average blood pressure for people 30 years old is 120, while for those 50 years old the average is 130.a. What is the slope of the regression line?b. What is the estimated average systolic blood pressure
3.19 A regression equation for y 5 handspan (cm) and x 5 height (inches) was discussed in Section 3.2. If the roles of the variables are reversed and only women are considered, the regression equation is Average height 5 51.1 1 0.7 (Handspan).a. Interpret the slope of 0.7 in terms of how height
3.18 The average August temperatures (y) and geographic latitudes (x) of 20 cities in the United States were given in the table for Exercise 3.9. (The data are part of the temperature dataset on the companion website.) The regression equation for these data is y^ 5 113.6 2 1.01xa. What is the slope
3.17 The equation for converting a temperature from x 5 degrees Celsius to y 5 degrees Fahrenheit is y 5 32 1 1.8x. Does this equation describe a statistical relationship or a deterministic relationship? Briefly explain your answer.General Section Exercises
3.16 A school cafeteria has a salad bar that is priced based on weight, with salads costing 30 cents an ounce. Students fill a container that weighs 8 ounces when it is empty. Define x to be the weight of the filled container (in ounces) and y to be the price the student is charged (in dollars).
3.15 Refer to the scatterplot for Exercise 3.3 showing the relationship between the average math SAT score and the percentage of high school graduates taking the test for the 50 states and District of Columbia. (The data are from the sats98 dataset on the companion website.) The regression line for
3.14 Refer to Exercise 3.13 in which a regression equation is given that relates average weight and height for men in the 18- to 29-year-old age group.a. Suppose a man in this age group is 72 inches tall. Use the regression equation given in the previous exercise to predict the weight of this
3.13 Suppose that a regression equation for the relationship between y 5 weight (pounds) and x 5 height (inches) for men aged 18 to 29 years old is Average weight 5 2250 1 6 (Height)a. Estimate the average weight for men in this age group who are 70 inches tall.b. What is the slope of the
3.12 The following table shows sex, height (inches), and midparent height (inches) for a sample of 18 college students.The variable mid-parent height is the average of mother’s height and father’s height. (These data are in the dataset UCDchap3 on the companion website; they are sampled from
3.11 The data in the following table show the square footage and asking price (in thousands of dollars) for nine homes for sale in Orange County, California in February 2010. Orange County has a mixture of residential areas, including suburban neighborhoods and exclusive beachfront properties.a. In
3.10 Refer to the latitude and temperature data in the table presented in Exercise 3.9, which also appear in the temperature dataset on the companion website.a. Draw a scatterplot of y 5 January temperature versus x 5 latitude.b. Is the pattern linear or curved?c. Is the direction of the
3.9 The data in the following table are the geographic latitudes and the average August and January temperatures (Fahrenheit)for 20 cities in the United States. The cities are listed in geographic order from south to north. (These data are part of the temperature dataset on the companion
3.8 The figure for this exercise is a scatterplot of y 5 pulse rate after marching in place for 1 minute versus x 5 resting pulse rate measured before marching in place. (The data are in the pulsemarch dataset on the companion website.)105 100 95 90 85 80 75 70 65 60 Pulse after marching Pulse
3.7 The following table shows the relationship between the speed of a car (mph) and the average stopping distance(feet) after the brakes are applied:Speed (mph) 0 10 20 30 40 50 60 70 Distance (ft) 0 20 50 95 150 220 300 400 Source: Defensive Driving: Managing Time and Space, American Automobile
3.6 Identify whether a scatterplot would or would not be an appropriate visual summary of the relationship between the following variables. In each case, explain your reasoning.a. Verbal SAT score and math SAT score.b. Handspan and sex (male or female).General Section Exercises
3.5 Identify whether a scatterplot would or would not be an appropriate visual summary of the relationship between the following variables. In each case, explain your reasoning.a. Blood pressure and age.b. Region of country and opinion about stronger gun control laws.
3.4 The figure for this exercise is a scatterplot of y 5 head circumference (cm) versus x 5 height (inches) for the 30 females in the physical dataset on the companion website.61 60 59 58 57 56 55 54 53 Head circumference (cm)Height (in.)60 62 64 66 68 70 72a. Does the plot show a positive
3.3 The figure for this exercise is a scatterplot of y 5 average math SAT score in 1998 versus x 5 percent of graduating seniors who took the test that year for the 50 states and the District of Columbia. The data are from the sats98 dataset on the companion website.600 575 550 525 500 475 Average
3.2 For each of the following pairs of variables, is there likely to be a positive association, a negative association, or no association? Briefly explain your reasoning.a. Miles of running per week and time for a 5-kilometer run.b. Forearm length and foot length.c. Grade level and height for
3.1 For each of the following pairs of variables, is there likely to be a positive association, a negative association, or no association?Briefly explain your reasoning.a. Amount of alcohol consumed and performance on a test of coordination, where a high score represents better coordination.b.
2.144 Use the GSS-08 dataset on the companion website. The variable degree indicates the highest educational degree achieved by a respondent.a. Is the degree variable quantitative, categorical, or ordinal?Explain.b. Determine the number and percentage falling into each degree category.c. What
2.143 Use the pennstate1 dataset on the companion website for this exercise.a. Draw a histogram of the height variable.b. What is the shape of this histogram? Why do you think it is not a bell shape?c. Draw a boxplot of the height variable.d. Which graph, the histogram or the boxplot, is more
2.142 Use the cholest dataset on the companion website for this exercise. The dataset contains cholesterol levels for 30 “control”patients and 28 heart attack patients at a medical facility.For the heart attack patients, cholesterol levels were measured 2 days, 4 days, and 14 days after the
2.141 For this exercise, use the GSS-08 dataset on the companion website. The variable cappun is the respondent’s opinion about the death penalty for persons convicted of murder, and the variable polparty is the respondent’s political party preference (Democrat, Republican, Independent,
2.140 Use the pennstate2 dataset on the companion website for this exercise. The variable CDs is the approximate number of music CDs owned by a student.a. Draw a stem-and-leaf plot for the CDs variable.b. Draw a histogram for the CDs variable.c. Draw a dotplot for the CDs variable.d. Describe the
2.139 Use the pennstate1 dataset on the companion website for this exercise. The data for the variable HrsSleep are responses by n 190 students to the question, “How many hours did you sleep last night?”a. Draw a histogram of the data for the HrsSleep variable.Describe the shape of this
2.138 The data for this exercise are in the GSS-08 dataset on the companion website. The variable gunlaw is whether a respondent favors or opposes stronger gun control laws.a. Determine the percentage of respondents who favor stronger gun control laws and the percentage of respondents who oppose
2.137 Use the oldfaithful dataset on the companion website; it gives data for n 299 eruptions of the Old Faithful geyser.a. The variable TimeToNext is the time until the next eruption after the present eruption. Draw a histogram of this variable. Describe the shape of the histogram.b. Draw a
2.136 Explain why women’s heights are likely to have a bell shape but their ages at marriage do not.Dataset Exercises Datasets required to solve these exercises are available on the companion website, http://www.cengage.com/statistics/Utts5e.
2.135 The interquartile range and the standard deviation are two different measures of spread. Which measure do you think is more affected by outliers? Explain.
2.134 Refer to Exercise 2.40, which gives a five-number summary of heights for college women. Draw a boxplot displaying the information in this five-number summary.
2.133 Exercise 2.65 gave the following weights (in pounds) for nine men on the Cambridge crew team:188.5, 183.0, 194.5, 185.0, 214.0, 203.5, 186.0, 178.5, 109.0 Draw a boxplot of these data.
2.132 In each case, specify which of the two variables is the explanatory variable and which is the response variable. If it is ambiguous, explain why.a. Is there a relationship between eye color and whether or not corrective lenses are needed by age 18?b. For women who are HIV-positive when they
2.131 Exercise 2.46 gave the following data values for the number of CDs owned by 24 students in a statistics class (in 1999). (Data source: musiccds dataset on the companion website.)220, 20, 50, 450, 300, 30, 20, 50, 200, 35, 25, 50, 250, 100, 0, 100, 20, 13, 200, 2, 125, 150, 90, 60a. Find the
2.130 Individuals are a representative sample of college students.Two variables: Male or female and whether the person dreams in color (yes or no).
2.129 Individuals are a representative sample of adults in a large city.Two variables: Ounces of coffee consumed per day and marital status (currently married or not).
2.128 Individuals are all mathematics majors at a college.Two variables: Grade point average and hours spent studying last week.
2.127 Individuals are all of the kindergarten children in a school district.One variable: Adult(s) with whom the child lives (both parents, mother only, father only, one or both grandparents, other).
2.126 For a bell-shaped dataset with a large number of values, approximately what z-score would correspond to a data value equaling each of the following?a. The median.b. The lowest value.c. The highest value.d. The mean.Exercises 2.127 to 2.130 each describe one or two variables and the
2.125 Refer to Exercise 2.52, in which the ages for the highestpaid 50 CEOs of America’s top 500 companies were given.These data are in the ceodata08 dataset for this book.a. Find the mean and standard deviation for these ages.b. Recall that the range should be equivalent to 4 to 6 standard
2.124 For each of the following two sets of data, explain which one is likely to have a larger standard deviation:a. Set 1: Heights of the children in a kindergarten class.Set 2: Heights of all of the children in an elementary school.b. Set 1: Systolic blood pressure for a single individual taken
2.123 The data for 103 women’s right handspans are shown in Figures 2.7 to 2.9 (p. 29), and a five-number summary is given in Example 2.5 (p. 25).a. Examine Figures 2.7 to 2.9 and comment on whether or not the Empirical Rule should hold.b. The mean and standard deviation for these measurements
2.122a. If a data value has a z-score of 0, the value equals one of the summary measures discussed in this chapter. Which summary measure is that?b. Verify that a data value having a z-score of 1.0 is equal to the mean plus 1 standard deviation.
2.121 In each case, specify which of the two variables is the explanatory variable and which is the response variable. If it is ambiguous, explain why.a. Is there a relationship between the amount of beer people drink and their systolic blood pressure?b. Is there a relationship between calories of
2.120 Each of the following quotes is taken from an article titled,“Education seems to help in selecting husbands” (Sacramento Bee, December 4, 1998, p. A21), which reported on data in the Statistical Abstract of the United States. Draw an appropriate graph to represent each situation.a. “The
2.119a. Would the first ladies’ ages at death data in Table 2.5(p. 27) be considered a population of measurements or a sample from some larger population? Explain.b. Find the appropriate standard deviation (sample or population) for the “ages at death” data in Table 2.5(p. 27).
2.118 Look around your living space or current surroundings and find a quantitative variable for which you can collect at least 20 observations (examples: number of words in the titles of books or your last 20 scores on tests and homework assignments). List the data with your response.a. Create a
2.117 A sample of n 500 individuals is asked how many hours they typically spend watching movies in a week. The mean response is x 8.3 hours, and the standard deviation is s 7.2 hours. Find values for the interval x ± 2s, and explain why the result is evidence that the distribution of weekly
2.116 Look around your living space or current surroundings, and find a categorical variable for which there are at least three categories and for which you can collect at least 20 observations(example: color of the shirts in your closet). Collect the data.a. Draw a pie chart for your data.b. Draw
2.115 For each of the following datasets, explain whether you would expect the mean or the median of the observations to be higher:a. In a rural farming community, for each household the number of children is measured.b. For all households in a large city, yearly household income is measured.c. For
2.114 Reach into your wallet, pocket, or wherever you can find at least ten coins, and sort all of the coins you have by type.a. Count how many of each kind of coin you have (pennies, nickels, and so on, or the equivalent for your country).Draw a pie chart illustrating the distribution of your
2.113 Can a variable be both of the following types? If so, give an example.a. An explanatory variable and a categorical variable.b. A continuous variable and an ordinal variable.c. A quantitative variable and a response variable.d. A bell-shaped variable and a response variable.
2.112 In the same survey for which wives’ heights are given in Example 2.19, husbands’ heights were also recorded. A fivenumber summary of husbands’ heights (mm) follows:Husbands’ Heights(n 199)Median 1725 Quartiles 1691 1774 Extremes 1559 1949a. Construct a boxplot for the husbands’
2.111 Specify the type (categorical, ordinal, quantitative) for each of the following variables recorded in a survey of cell phone usage among students:a. Telephone exchange (first three numbers after area code).b. Number of text messages sent last month.c. Dollar amount of last month’s phone
2.110 For each of the following situations, would you prefer your value to be average, a low outlier, or a high outlier? Explain.a. Number of children you have.b. Your annual salary.c. Gas mileage for your car in miles driven per gallon of gas.d. Crime rate in the city or town where you live.
2.109 A question in the 2002 General Social Survey (GSS) conducted by the National Opinion Research Center asked participants how long they spend on e-mail each week. A summary of responses (hours) for n 1881 respondents follows. (The data are in the dataset GSS-02 on the companion website.)Mean
2.108 Remember that a resistant statistic is a numerical summary whose value is not unduly influenced by an outlier of any magnitude. Is the standard deviation a resistant statistic?Justify your answer by giving an example of a small dataset, and then adding a very large outlier and noting how the
2.107 Can a categorical variable have a bell-shaped distribution?Explain.
2.106 Using a computer or calculator that provides proportions falling below a specified z-score, determine the approximate proportion for each of the following situations. In each case, assume the values are approximately bell-shaped.a. The proportion of SAT scores falling below 450 for a group
2.105 Exercise 2.103 gave the information that the verbal SAT scores for students admitted to a university had a bell-shaped distribution with mean 540 and standard deviation 50.a. What is the verbal SAT score such that only 16% of admitted students had a higher score?b. What is the verbal SAT
2.104 Exercise 2.101 gave the information that head circumferences of adult males have a bell-shaped distribution with mean 56 cm and standard deviation 2 cm.a. What is the head circumference such that only 2.5% of adult males have a smaller head circumference?b. What is the head circumference
2.103 Suppose verbal SAT scores for students admitted to a university are bell-shaped with a mean of 540 and a standard deviation of 50.a. Draw a picture of the distribution of these verbal SAT scores, indicating the cutoff points for the middle 68%, 95%, and 99.7% of the scores.b. What is the
2.102 Refer to Exercise 2.101. What is the variance of head circumferences of adult males?
2.101 Head circumferences of adult males have a bell-shaped distribution with a mean of 56 cm and a standard deviation of 2 cm.a. Explain whether or not it would be unusual for an adult male to have a 52-cm head circumference.b. Explain whether or not it would be unusual for an adult male to have a
2.100 Refer to the women’s right handspan data in Table 2.4. As you can see in Figures 2.7 to 2.9, there are two apparent outliers at 12.5 cm and 13.0 cm.a. If these values are removed, do you think the mean will increase, decrease, or remain the same? What about the standard deviation?
2.99 The mean for the women’s right handspans in Table 2.4 is about 20 cm, with a standard deviation of about 1.8 cm. Using the stem-and-leaf plot in Figure 2.8 (p. 29), determine how well this set of measurements fits with the Empirical Rule.
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