# Chapter 2: Looking at Data—Relationships Chapter 2: Looking at Data Relationships 2017 W. H. Freeman and Company 2.1-1 I want to examine the relationship between gas mileage of cars and engine size (displacement in cubic inches). The explanatory variable is a. engine size. b. gas mileage. c. either one can be used. 2.1 Relationships 2.1-1 answer I want to examine the relationship between gas mileage of cars and engine size (displacement in cubic inches). The explanatory variable is a. engine size. (correct) b. gas mileage.

c. either one can be used. 2.1 Relationships 2.1-2 A researcher would like to know if a mothers height can explain how tall her child will be. Which is the response variable? a. childs height b. mothers height c. fathers height 2.1 Relationships 2.1-2 answer A researcher would like to know if a mothers height can explain how tall her child will be. Which is the response variable? a. childs height (correct) b. mothers height

c. fathers height 2.1 Relationships 2.1-3 If interest lies in looking at the relationship between hours of study and grade on an exam, the explanatory variable is a. hours of study. b. grade on exam. c. either one can be used. 2.1 Relationships 2.1-3 answer If interest lies in looking at the relationship between hours of study and grade on an exam, the explanatory variable is a. hours of study. (correct) b. grade on exam.

c. either one can be used. 2.1 Relationships 2.2-1 A major study examined the relationship between cause of death (heart attack, cancer, stroke, accident, etc.) and age. A good way to graphically represent the relationship is with a. side-by-side boxplots. b. back-to-back stemplots. c. a scatterplot. 2.2 Scatterplots 2.2-1 answer A major study examined the relationship between cause of death (heart attack, cancer, stroke, accident, etc.) and age. A good way to graphically represent the relationship is with

a. side-by-side boxplots. (correct) b. back-to-back stemplots. c. a scatterplot. 2.2 Scatterplots 2.2-2 I want to examine whether or not there is a relationship between a students grade point average and after-college plans. For a visual display of the data, I should choose a. a scatterplot. b. side-by-side boxplots. c. a back-to-back stemplot. 2.2 Scatterplots 2.2-2 answer I want to examine whether or not there is a relationship between a students grade point

average and after-college plans. For a visual display of the data, I should choose a. a scatterplot. b. side-by-side boxplots. (correct) c. a back-to-back stemplot. 2.2 Scatterplots 2.2-3 At a large department store, the amount a shopper spent and the shoppers gender (male or female) were recorded. To determine if gender is useful in explaining the amount of money a shopper spends at the store, we could a. make side-by-side boxplots of the distribution of the amount spent by males and the distribution of the amount spent by females. b. compute the correlation between the amount spent and gender. c. compute the least-squares regression line of amount spent by gender.

2.2 Scatterplots 2.2-3 answer At a large department store, the amount a shopper spent and the shoppers gender (male or female) were recorded. To determine if gender is useful in explaining the amount of money a shopper spends at the store, we could a. make side-by-side boxplots of the distribution of the amount spent by males and the distribution of the amount spent by females. (correct) b. compute the correlation between the amount spent and gender. c. compute the least-squares regression line of amount spent by gender. 2.2 Scatterplots 2.2-4 Describe the pattern of the below scatterplot.

Y 60 50 40 30 20 10 0 0 2 4 6 8 10

12 14 a. strong negative relationship b. strong positive relationship c. weak negative relationship 2.2 Scatterplots 2.2-4 answer Describe the pattern of the below scatterplot. Y 60 50 40 30 20 10 0 0

2 4 6 8 10 12 14 a. strong negative relationship b. strong positive relationship (correct) c. weak negative relationship 2.2 Scatterplots

2.2-5 Describe the pattern of the below scatterplot. a. weak positive relationship b. strong positive relationship c. weak negative relationship 2.2 Scatterplots 2.2-5 answer Describe the pattern of the below scatterplot. a. weak positive relationship (correct) b. strong positive relationship c. weak negative relationship 2.2 Scatterplots 2.3-1 A recent article in an educational research journal reports a correlation of +0.8 between math achievement and overall math aptitude. It also reports a correlation of 0.8

between math achievement and a math anxiety test. Which of the following interpretations is the most correct? a. The correlation of +0.8 indicates a stronger relationship than the correlation of 0.8. b. The correlation of +0.8 is just as strong as the correlation of 0.8. c. It is impossible to tell which correlation is stronger. 2.3 Correlation 2.3-1 answer A recent article in an educational research journal reports a correlation of +0.8 between math achievement and overall math aptitude. It also reports a correlation of 0.8 between math achievement and a math anxiety test. Which of the following interpretations is the most correct? a. The correlation of +0.8 indicates a stronger relationship than the correlation of 0.8. b. The correlation of +0.8 is just as strong as the correlation of 0.8. (correct)

c. It is impossible to tell which correlation is stronger. 2.3 Correlation 2.3-2 Are the following two variables positively associated, negatively associated or not associated? Let x be how much gas you have in your tank (in gallons). Let y be the cost to fill your gas tank. a. The two variables are positively associated. b. The two variables are negatively associated. c. The two variables are not associated. 2.3 Correlation 2.3-2 answer Are the following two variables positively associated, negatively associated or not associated? Let x be how much gas you have in your tank (in gallons). Let y be the cost to fill your gas tank.

a. The two variables are positively associated. b. The two variables are negatively associated. (correct) c. The two variables are not associated. 2.3 Correlation 2.3-3 A researcher measures a response variable y and explanatory variable x on each of several objects. A scatterplot of the measurements is as follows. The researcher notices that there is a distinct curved pattern in the plot. It would be appropriate to conclude y x a. r is small. b. r is approximately 2/3 because y decreases as x increases in approximately 2/3 of the plot. c. r is meaningless here.

2.3 Correlation 2.3-3 answer A researcher measures a response variable y and explanatory variable x on each of several objects. A scatterplot of the measurements is as follows. The researcher notices that there is a distinct curved pattern in the plot. It would be appropriate to conclude y x a. r is small. b. r is approximately 2/3 because y decreases as x increases in approximately 2/3 of the plot. c. r is meaningless here. (correct) 2.3 Correlation 2.3-4 On this slide is a plot of the Olympic gold-medal-winning performance

in the high jump (in inches) for the years 1900 to 1996. From this plot, the correlation between the winning height and year of the jump is a. about 0.95. b. about 0.10. c. about 0.50. 2.3 Correlation 2.3-4 answer On this slide is a plot of the Olympic gold-medal-winning performance in the high jump (in inches) for the years 1900 to 1996. From this plot, the correlation between the winning height and year of the jump is a. about 0.95. (correct) b. about 0.10. c. about 0.50. 2.3 Correlation

2.3-6 I wish to determine the correlation between the height (in inches) and weight (in pounds) of 21-year-old males. To do this, I measure the height and weight of two 21-year-old men. The measured values are Male #1 Male #2 Height 70 69 Weight 160 164

The correlation, r, computed from the measurements on these males, is a. 1.0. b. 1.0. c. near 0, because the heights and weights of the men are similar. 2.3 Correlation 2.3-6 answer I wish to determine the correlation between the height (in inches) and weight (in pounds) of 21-year-old males. To do this, I measure the height and weight of two 21-year-old men. The measured values are Male #1 Male #2 Height 70 69

Weight 160 164 The correlation, r, computed from the measurements on these males, is a. 1.0. b. 1.0. (correct) c. near 0, because the heights and weights of the men are similar. 2.3 Correlation 2.3-7 For the below plot, approximate the correlation. y a. about 0.7 b. about 0.05

c. about 0.6 2.3 Correlation 2.3-7 answer For the below plot, approximate the correlation. y a. about 0.7 (correct) b. about 0.05 c. about 0.6 2.3 Correlation 2.4-1 A chemist was conducting an experiment to find how many ml of a particular substance dissolves in different temperatures of water. A correlation of 0.87 was computed. Which interpretation is TRUE? a. 87% of the variation in the amount of dissolved substance is explained by temperature. b. Correlation cannot be computed because temperature is

not a continuous variable. c. 76% of the variation in the amount of dissolved substance is explained by temperature. 2.4 Least-Squares Regression 2.4-1 answer A chemist was conducting an experiment to find how many ml of a particular substance dissolves in different temperatures of water. A correlation of 0.87 was computed. Which interpretation is TRUE? a. 87% of the variation in the amount of dissolved substance is explained by temperature. b. Correlation cannot be computed because temperature is not a continuous variable. c. 76% of the variation in the amount of dissolved substance is explained by temperature. (correct) 2.4 Least-Squares Regression

2.4-2 Below is a plot of the Olympic gold-medal-winning performance in the high jump (in inches) for the years 1900 to 1996. The equation of the least-squares regression line of Winning Height (in inches) on Year is Winning Height = 364.90 + 0.23 Year In another millennium (the year 3000), if the Olympics continue to be held, we can expect the Winning Height to be about a. 325 inches. b. 690 inches. c. none of the above. 2.4 Least-Squares Regression 2.4-2 answer Below is a plot of the Olympic gold-medal-winning performance in the high jump (in inches) for the years 1900 to 1996. The equation of the least-squares regression line of Winning Height (in inches) on Year is Winning Height = 364.90 + 0.23 Year In another millennium (the year 3000), if the Olympics continue to be

held, we can expect the Winning Height to be about a. 325 inches. b. 690 inches. c. none of the above. (correct) (Predicted valueheight >27 ft. is not plausible-extrapolation) 2.4 Least-Squares Regression 2.4-3 The regression line to predict the average exam grade from hours of study is . The slope of the regression line indicates: a. for any student, an extra hour of study is predicted to increase the grade 5.6 points. b. on average, an extra hour of study is predicted to increase the grade 5.6 points. c. an extra hour of study will increase the grade 15 points. 2.4 Least-Squares Regression

2.4-3 answer The regression line to predict the average exam grade from hours of study is . The slope of the regression line indicates: a. for any student, an extra hour of study is predicted to increase the grade 5.6 points. b. on average, an extra hour of study is predicted to increase the grade 5.6 points. (correct) c. an extra hour of study will increase the grade 15 points. 2.4 Least-Squares Regression 2.4-4 Which of the following statements would be a valid conclusion from this plot of record times for men and women in some sports? O = men X = women

a. The world record times for women show a greater rate of improvement (decrease more rapidly) than the world record times for men. b. We can expect the world record times for women to be lower than those for men sometime before the year 2010. c. By the year 2010, the world record times for men will reach a plateau beyond which no improvement will be possible. 2.4 Least-Squares Regression 2.4-4 answer Which of the following statements would be a valid conclusion from this plot of record times for men and women in some sports? O = men X = women a. The world record times for women show a greater rate of improvement (decrease more rapidly) than the world record times for men. (correct)

b. We can expect the world record times for women to be lower than those for men sometime before the year 2010. c. By the year 2010, the world record times for men will reach a plateau beyond which no improvement will be possible. 2.4 Least-Squares Regression 2.4-5 Which of the following measures only the strength of a relationship? a. the correlation coefficient b. the slope c. the coefficient of determination 2.4 Least-Squares Regression 2.4-5 answer Which of the following measures only the strength of a relationship? a. the correlation coefficient b. the slope

c. the coefficient of determination (correct) 2.4 Least-Squares Regression 2.4-6 Which of the following is correct with respect to the correlation coefficient (r) and the slope of the leastsquares regression line? a. They will always have the same sign. b. They will have opposite signs. c. Nothing, because they are two different measures that are not related to one another. 2.4 Least-Squares Regression 2.4-6 answer Which of the following is correct with respect to the correlation coefficient (r) and the slope of the leastsquares regression line? a. They will always have the same sign. (correct) b. They will have opposite signs.

c. Nothing, because they are two different measures that are not related to one another. 2.4 Least-Squares Regression 2.4-7 Assume that the relationship between x = the prevailing mortgage interest rates and y = the number of new houses being built per month in a Midwestern city given by the least-squares regression equation is Number of new houses = 672.89 30.65 interest rate and r = 0.7 Assuming that a linear model is appropriate, which of the following descriptions below best represent the value of the slope? a. When no new houses are being built, the interest rate equals 30.65%. b. When the number of new houses being built increases by 1, the interest rate is expected to drop by 0.3065. c. When the interest rate increases by 1%, the number of new houses being built is expected to drop by 30.65. d. We cannot interpret the slope because we cannot build a negative number of new houses. 2.4 Least-Squares Regression

2.4-7 answer Assume that the relationship between x = the prevailing mortgage interest rates and y = the number of new houses being built per month in a Midwestern city given by the least-squares regression equation is Number of new houses = 672.89 30.65 interest rate and r = 0.7 Assuming that a linear model is appropriate, which of the following descriptions below best represent the value of the slope? a. When no new houses are being built, the interest rate equals 30.65%. b. When the number of new houses being built increases by 1, the interest rate is expected to drop by 0.3065. c. When the interest rate increases by 1%, the number of new houses being built is expected to drop by 30.65. (correct) d. We cannot interpret the slope because we cannot build a negative number of new houses. 2.4 Least-Squares Regression 2.4-8 Assume that the relationship between x = the prevailing mortgage interest rates and y = the number

of new houses being built per month in a Midwestern city given by the least-squares regression equation is Number of new houses = 672.89 30.65 interest rate and r = 0.7 Assuming that a linear model is appropriate, which of the following interpretations of the information given is most correct? a. There is no association between x and y. b. Negative, fairly strong linear relationship. 70% of the variation in the number of new houses is explained by the prevailing interest rates. c. Positive, fairly strong linear relationship. 70% of the variation in the number of new houses is explained by the prevailing interest rates. d. Negative, fairly strong linear relationship. 49% of the variation in the number of new houses is explained by the prevailing interest rates. e. Positive, fairly strong linear relationship. 49% of the variation in the number of new houses is explained by the prevailing interest rates. 2.4 Least-Squares Regression 2.4-8 answer Assume that the relationship between x = the prevailing mortgage interest rates and y = the number of new houses being built per month in a Midwestern city given by the least-squares regression

equation is Number of new houses = 672.89 30.65 interest rate and r = 0.7 Assuming that a linear model is appropriate, which of the following interpretations of the information given is most correct? 2 a. There is no association between x and y. r 0.49 b. Negative, fairly strong linear relationship. 70% of the variation in the number of new houses is explained by the prevailing interest rates. c. Positive, fairly strong linear relationship. 70% of the variation in the number of new houses is explained by the prevailing interest rates. d. Negative, fairly strong linear relationship. 49% of the variation in the number of new houses is explained by the prevailing interest rates. (correct) e. Positive, fairly strong linear relationship. 49% of the variation in the number of new houses is explained by the prevailing interest rates. 2.4 Least-Squares Regression

2.4-9 Which of the following statements about the least-squares regression line is/are TRUE? (I) The slope of the least-squares regression line always has the same sign as the correlation coefficient. (II) The least-squares regression line is the line that minimizes the sum of the squares of the residuals. (III) The least-squares regression line is the line that maximizes the sum of the squares of the residuals. a. I only b. II only c. I and II only d. I and III only e. I, II, and III 2.4 Least-Squares Regression 2.4-9 answer Which of the following statements about the least-squares regression line is/are TRUE? (I) The slope of the least-squares regression line always has the same sign as the

correlation coefficient. (II) The least-squares regression line is the line that minimizes the sum of the squares of the residuals. (III) The least-squares regression line is the line that maximizes the sum of the squares of the residuals. a. I only b. II only c. I and II only (correct) d. I and III only e. I, II, and III 2.4 Least-Squares Regression 2.4-10 We have examined the age (x) and price (y) of a certain model of car. The age (in years) and price (in \$) for a sample of 15 cars yielded the following equation: What is the predicted selling price for a five-year-old car?

a. \$9400 b. \$9600 c. \$9800 d. \$10,000 e. \$10,200 2.4 Least-Squares Regression 2.4-10 answer We have examined the age (x) and price (y) of a certain model of car. The age (in years) and price (in \$) for a sample of 15 cars yielded the following equation: What is the predicted selling price for a five-year-old car? a. \$9400 b. \$9600 (correct) \$18,600 \$1800(5) = \$9600 c. \$9800 d. \$10,000 e. \$10,200 2.4 Least-Squares Regression

2.5-1 Refer to the question in the previous slide. What is the residual of a five-year-old car with a selling price of \$9000? a. \$600 b. \$600 c. \$1200 d. \$1200 e. cannot be calculated 2.5 Cautions about Correlation and Regression 2.5-1 answer Refer to the question in the previous slide. What is the residual of a five-year-old car with a selling price of \$9000? a. \$600 (correct) b. \$600 c. \$1200

y 18600 1800(5) 9600 residual y y residual 9000 9600 600 d. \$1200 e. cannot be calculated 2.5 Cautions about Correlation and Regression 2.5-2 A researcher examines data from all cities with populations over 100,000 in the United States. He notes that those cities with a major league baseball team tend to have a greater number of divorces than other cities. One can reasonably conclude that a. the presence of a major league baseball team contributes to divorce. Men spend time at the ballpark at the expense of their marriage.

b. this correlation cannot be explained and is probably accidental. Cities with major league baseball teams should have no more divorces than other cities. c. none of the above. 2.5 Cautions about Correlation and Regression 2.5-2 answer A researcher examines data from all cities with populations over 100,000 in the United States. He notes that those cities with a major league baseball team tend to have a greater number of divorces than other cities. One can reasonably conclude that a. the presence of a major league baseball team contributes to divorce. Men spend time at the ballpark at the expense of their marriage. b. this correlation cannot be explained and is probably accidental. Cities with major league baseball teams should have no more divorces than other cities. c. none of the above. (correct)

(Major league teams tend to be in the largest cities. Larger cities have more people and, hence, more divorces.) 2.5 Cautions about Correlation and Regression 2.5-3 A survey of 1000 adults ages 30 to 35 is conducted. The number of years of schooling and the annual salary for each person in the survey is recorded. The correlation between years of schooling and annual salary is found to be 0.27. Suppose, instead, the average salary of all individuals in the survey with the same number of years of schooling was calculated and the correlation between these averages and years of schooling was computed. This correlation would most likely be a. equal to 0.27. b. larger than 0.27. c. less than 0.27. 2.5 Cautions about Correlation and Regression

2.5-3 answer A survey of 1000 adults ages 30 to 35 is conducted. The number of years of schooling and the annual salary for each person in the survey is recorded. The correlation between years of schooling and annual salary is found to be 0.27. Suppose, instead, the average salary of all individuals in the survey with the same number of years of schooling was calculated and the correlation between these averages and years of schooling was computed. This correlation would most likely be a. equal to 0.27. b. larger than 0.27. (correct) c. less than 0.27. 2.5 Cautions about Correlation and Regression 2.5-4 In the graph to the right, the circled point is

a. an influential point. Deleting it should reduce the correlation and improve the fit. b. not an influential point because its y value is not unusually large or small. c. an influential point. Deleting it should increase the estimate of the slope. 2.5 Cautions about Correlation and Regression 2.5-4 answer In the graph to the right, the circled point is a. an influential point. Deleting it should reduce the correlation and improve the fit. b. not an influential point because its y value is not unusually large or small. c. an influential point. Deleting it should increase the estimate of the slope. (correct)

2.5 Cautions about Correlation and Regression 2.5-5 A student has obtained the following computer output from a regression examining the relationship between BTU input to a furnace and the BTU output: We can conclude from this information that a. the regression is useful because R-squared is large. b. the regression model is not useful because the slope is small. c. we do not have enough information to conclude whether or not the regression is useful. 2.5 Cautions about Correlation and Regression 2.5-5 answer A student has obtained the following computer output from a regression examining the relationship between BTU input to a furnace and the BTU output:

We can conclude from this information that a. the regression is useful because R-squared is large. b. the regression model is not useful because the slope is small. c. we do not have enough information to conclude whether or not the regression is useful. (correct) (We cannot make a conclusion about whether the model is useful without checking residuals plots.) 2.5 Cautions about Correlation and Regression 2.5-6 A student has obtained the following computer output from a regression examining the relationship between BTU input to a furnace and the BTU output: Assuming the regression is appropriate, we conclude a. for every BTU input to a furnace, the output increases by 0.911, on average.

b. for every 0.187 BTU input to a furnace, the output increases by 0.911, on average. c. for every 0.911 BTU input to a furnace, the output increases by 1, on average. 2.5 Cautions about Correlation and Regression 2.5-6 answer A student has obtained the following computer output from a regression examining the relationship between BTU input to a furnace and the BTU output: Assuming the regression is appropriate, we conclude a. for every BTU input to a furnace, the output increases by 0.911, on average. (correct) b. for every 0.187 BTU input to a furnace, the output increases by 0.911, on average. c. for every 0.911 BTU input to a furnace, the output increases by 1, on average. 2.5 Cautions about Correlation and

Regression 2.6-1 A study was conducted to assess the effect of the drug Imipramine on the treatment of patients with agoraphobia and panic disorder. The treatment groups included a control group, a group treated with a dose of 1.5 mg/kg of body weight and a group treated with a dose of 3 mg/kg of body weight. There were 70 subjects. At the end of 24 weeks of treatment, subjects were classified as responders or non-responders to treatment based on a battery of psychological tests shown in the table. The proportion of responders in the experiment is a. 0.3428. Responder? b. 0.3667. Treatment Yes

No c. 0.4500. Control 6 24 1.5 mg/kg 9 11 3 mg/kg 9

11 2.6 Data Analysis for Two-Way Tables 2.6-1 answer A study was conducted to assess the effect of the drug Imipramine on the treatment of patients with agoraphobia and panic disorder. The treatment groups included a control group, a group treated with a dose of 1.5 mg/kg of body weight and a group treated with a dose of 3 mg/kg of body weight. There were 70 subjects. At the end of 24 weeks of treatment, subjects were classified as responders or non-responders to treatment based on a battery of psychological tests shown in the table. The proportion of responders in the experiment is a. 0.3428. (correct) b. 0.3667. c. 0.4500. 24 70

Responder? Treatment Yes Control 6 1.5 mg/kg 9 3 mg/kg 9 24 2.6 Data Analysis for Two-Way Tables

2.6-2 A study was performed to examine the personal goals of children in grades 4, 5, and 6. They were asked what they would most like to do at school: make good grades, be popular, or be good at sports. Results are presented in the table below by the sex of the child. Make good grades Be popular Be good in sports Boys 96 32 94 Girls

295 45 40 The proportion of girls who chose the goal Be good in sports is a. 40/380. b. 40/134. c. 40/602. 2.6 Data Analysis for Two-Way Tables 2.6-2 answer A study was performed to examine the personal goals of children in grades 4, 5, and 6. They were asked what they would most like to do at school: make good grades, be popular, or be good at sports. Results are presented in the table below by the sex of the child. Make good grades

Be popular Be good in sports Boys 96 32 94 Girls 295 45 40

380 (Girls Total) The proportion of girls who chose the goal Be good in sports is a. 40/380. (correct) b. 40/134. c. 40/602. 2.6 Data Analysis for Two-Way Tables 2.6-3 A large company has been sued for sex discrimination. The case brought by the female managers claimed they were underrepresented in management. However, further analysis of the company by division found that females were actually more likely than males to be managers in each division. This is an example of a. aggregating data. b. Simpsons paradox. c. biased data collection.

2.6 Data Analysis for Two-Way Tables 2.6-3 answer A large company has been sued for sex discrimination. The case brought by the female managers claimed they were underrepresented in management. However, further analysis of the company by division found that females were actually more likely than males to be managers in each division. This is an example of a. aggregating data. b. Simpsons paradox. (correct) c. biased data collection. 2.6 Data Analysis for Two-Way Tables 2.6-4 In the table below, we examine the relationship between final grade and the reported hours per week each student said they studied for the course. A

B C D E Total < 5 2 3 7 4 5 21 5 10 3 5 5 4 6 23 > 10

6 5 3 4 2 20 Total 11 13 15

12 13 64 According to the table, the probability that a random student both earned a C and studied between 5 and 10 hours per week is a. 15/64. b. 5/64. c. 23/64. 2.6 Data Analysis for Two-Way Tables 2.6-4 answer In the table below, we examine the relationship between final grade and the reported hours per week each student said they studied for the course. A

B C D E Total < 5 2 3 7 4

5 21 5 10 3 5 5 4 6 23 > 10

6 5 3 4 2 20 Total 11 13 15

12 13 64 According to the table, the probability that a random student both earned a C and studied between 5 and 10 hours per week is a. 15/64. b. 5/64. (correct) c. 23/64. 2.6 Data Analysis for Two-Way Tables 2.6-5 The ecology department head is examining course evaluations for four different sections of an introductory course taught last semester by four different instructors. He would like to know if the opinions of students are homogeneous with respect to the quality of instruction they received from their respective professors. Region Rating

Section 1 Section 2 Section 3 Section 4 Total Positive Rating 17 24 9 12

62 Negative Rating 8 5 7 10 30 Neutral Rating 9 6

16 16 47 Total 34 35 32 38 139 What proportion of all students are in Section 1 and feel neutral about the professor?

a. 0.0647 b. 0.1667 c. 0.4460 2.6 Data Analysis for Two-Way Tables 2.6-5 answer The ecology department head is examining course evaluations for four different sections of an introductory course taught last semester by four different instructors. He would like to know if the opinions of students are homogeneous with respect to the quality of instruction they received from their respective professors. Region Rating Section 1 Section 2 Section 3 Section 4

Total Positive Rating 17 24 9 12 62 Negative Rating 8 5

7 10 30 Neutral Rating 9 6 16 16 47 Total

34 35 32 38 139 What proportion of all students are in Section 1 and feel neutral about the professor? a. 0.0647 (correct) 9/139 = 0.0647 b. 0.1667 c. 0.4460 2.6 Data Analysis for Two-Way Tables 2.6-6

The ecology department head is examining course evaluations for four different sections of an introductory course taught last semester by four different instructors. He would like to know if the opinions of students are homogeneous with respect to the quality of instruction they received from their respective professors. Region Rating Section 1 Section 2 Section 3 Section 4 Total Positive Rating 17

24 9 12 62 Negative Rating 8 5 7 10 30

Neutral Rating 9 6 16 16 47 Total 34 35 32

38 139 What is the marginal proportion of positive ratings? a. 0.0647 b. 0.1667 c. 0.4460 2.6 Data Analysis for Two-Way Tables 2.6-6 answer The ecology department head is examining course evaluations for four different sections of an introductory course taught last semester by four different instructors. He would like to know if the opinions of students are homogeneous with respect to the quality of instruction they received from their respective professors. Region Rating Section 1

Section 2 Section 3 Section 4 Total Positive Rating 17 24 9 12 62

Negative Rating 8 5 7 10 30 Neutral Rating 9 6 16

16 47 Total 34 35 32 38 139 What is the marginal proportion of positive ratings? a. 0.0647 b. 0.1667

c. 0.4460 (correct) 62/139 = 0.4460 2.6 Data Analysis for Two-Way Tables 2.6-7 The ecology department head is examining course evaluations for four different sections of an introductory course taught last semester by four different instructors. He would like to know if the opinions of students are homogeneous with respect to the quality of instruction they received from their respective professors. Region Rating Section 1 Section 2 Section 3 Section 4

Total Positive Rating 17 24 9 12 62 Negative Rating 8 5

7 10 30 Neutral Rating 9 6 16 16 47 Total

34 35 32 38 139 What is the conditional probability of positive ratings given in Section 3? a. 0.0047 b. 0.1667 c. 0.2813 2.6 Data Analysis for Two-Way Tables 2.6-7 answer The ecology department head is examining course evaluations for four different sections of an introductory course taught last semester by four different instructors. He would like

to know if the opinions of students are homogeneous with respect to the quality of instruction they received from their respective professors. Region Rating Section 1 Section 2 Section 3 Section 4 Total Positive Rating 17 24

9 12 62 Negative Rating 8 5 7 10 30 Neutral Rating

9 6 16 16 47 Total 34 35 32 38

139 What is the conditional probability of positive ratings given in Section 3? a. 0.0047 b. 0.1667 c. 0.2813 (correct) 9/32 = 0.2813 2.6 Data Analysis for Two-Way Tables 2.6-8 The reversal of results when several groups are combined together to form a single group is known as a. confounding. b. Simpsons paradox. c. lurking variables. 2.6 Data Analysis for Two-Way Tables

2.6-8 answer The reversal of results when several groups are combined together to form a single group is known as a. confounding. b. Simpsons paradox. (correct) c. lurking variables. 2.6 Data Analysis for Two-Way Tables 2.7-1 A researcher notices that, in a sample of adults, those who take greater amounts of vitamin C have fewer illnesses. However, those who take greater amounts of vitamin C also tend to exercise more. As explanations for having fewer illnesses, the variables amount of vitamin C taken and amount of exercise are ____________ variables. a. skewed

b. confounding c. response d. symmetric 2.7 The Question of Causation 2.7-1 answer A researcher notices that, in a sample of adults, those who take greater amounts of vitamin C have fewer illnesses. However, those who take greater amounts of vitamin C also tend to exercise more. As explanations for having fewer illnesses, the variables amount of vitamin C taken and amount of exercise are ____________ variables. a. skewed b. confounding (correct) c. response d. symmetric 2.7 The Question of Causation 2.7-2

Which set of two variables is most likely to have a causeand-effect relationship? a. height of a person and the weight of a person b. weight of a box and the postage rate for shipping the box to California c. make of a car and the mileage of the car d. age of a teacher and the income of the teacher 2.7 The Question of Causation 2.7-2 answer Which set of two variables is most likely to have a causeand-effect relationship? a. height of a person and the weight of a person b. weight of a box and the postage rate for shipping the box to California (correct) c. make of a car and the mileage of the car d. age of a teacher and the income of the teacher 2.7 The Question of Causation

2.7-3 Which of the following would be necessary to establish a cause-and-effect relationship between two variables? a. Strong association between the variables would be necessary. b. An association between the variables in many different settings would be necessary. c. The alleged cause is plausible. d. all of the above 2.7 The Question of Causation 2.7-3 answer Which of the following would be necessary to establish a cause-and-effect relationship between two variables? a. Strong association between the variables would be necessary.

b. An association between the variables in many different settings would be necessary. c. The alleged cause is plausible. d. all of the above (correct) 2.7 The Question of Causation 2.7-4 When possible, what is the best way to establish that an observed association is the result of a cause-and-effect relationship? a. Study the least-squares regression line. b. Obtain the correlation coefficient. c. Use a well-designed experiment. d. Examine z-scores rather than the original variables. 2.7 The Question of Causation 2.7-4 answer

When possible, what is the best way to establish that an observed association is the result of a cause-and-effect relationship? a. Study the least-squares regression line. b. Obtain the correlation coefficient. c. Use a well-designed experiment. (correct) d. Examine z-scores rather than the original variables. 2.7 The Question of Causation 2.7-5 What is one of the main reasons it is difficult to conclude a cause-and-effect relationship? a. extrapolation of the data b. common responses c. lurking variables d. high values of the coefficient of determination

2.7 The Question of Causation 2.7-5 answer What is one of the main reasons it is difficult to conclude a cause-and-effect relationship? a. extrapolation of the data b. common responses c. lurking variables (correct) d. high values of the coefficient of determination 2.7 The Question of Causation 2.7-6 Which of the following diagrams is NOT an example of direct causation? a. causation b. common response

c. confounding 2.7 The Question of Causation 2.7-6 answer Which of the following diagrams is NOT an example of direct causation? a. causation b. common response c. confounding (correct) 2.7 The Question of Causation 2.7-7 When the effects on the response of two variables cannot be distinguished from each other,

this is referred to as a. Simpsons paradox. b. confounding. c. causation. 2.7 The Question of Causation 2.7-7 answer When the effects on the response of two variables cannot be distinguished from each other, this is referred to as a. Simpsons paradox. b. confounding. (correct) c. causation. 2.7 The Question of Causation