Ch. 3 practice ~ AP Stats
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31 Terms
1
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the height (in feet) and volume (in cubic feet) of usable lumber of 32 cherry trees are measured by a researcher. the goal is to determine if volume of usable lumber can be estimated from the height of a tree.
use scenario 3-1. which of the following statements are supported by the scatterplot?
i. there is a positive association between height and volume.
ii. there is an outlier in the plot.
iii. as the height of a cherry tree increases, the volume of useable lumber it yields increases.
A. i only
B. ii only
C. iii only
D. i and ii
E. i, ii, and iii
use scenario 3-1. which of the following statements are supported by the scatterplot?
i. there is a positive association between height and volume.
ii. there is an outlier in the plot.
iii. as the height of a cherry tree increases, the volume of useable lumber it yields increases.
A. i only
B. ii only
C. iii only
D. i and ii
E. i, ii, and iii
E. i, ii, and iii
2
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a study is conducted to determine if one can predict the yield of a crop based on the amount of fertilizer applied to the soil. the response variable in this study is…
A. yield of the crop.
B. amount of fertilizer applied to the soil.
C. the experimenter.
D. amount of rainfall.
E. the soil.
A. yield of the crop.
B. amount of fertilizer applied to the soil.
C. the experimenter.
D. amount of rainfall.
E. the soil.
A. yield of the crop
3
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two variables are said to be negatively associated if…
A. larger values of one variable are associated with larger values of the other.
B. larger values of one variable are associated with smaller values of the other.
C. smaller values of one variable are associated with smaller values of the other.
D. smaller values of one variable are associated with both larger or smaller values of the other.
E. there is no pattern in the relationship between the two variables.
A. larger values of one variable are associated with larger values of the other.
B. larger values of one variable are associated with smaller values of the other.
C. smaller values of one variable are associated with smaller values of the other.
D. smaller values of one variable are associated with both larger or smaller values of the other.
E. there is no pattern in the relationship between the two variables.
B. larger values of one variable are associated with smaller values of the other
4
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a study of the effects of television on child development measured how many hours of television each of 125 grade school children watched per week during a school year and each child's reading score. which variable would you put on the horizontal axis of a scatterplot of the data?
A. reading score, because it is the response variable
B. reading score, because it is the explanatory variable
C. hours of television, because it is the response variable
D. hours of television, because it is the explanatory variable
E. it makes no difference, because there is no explanatory-response distinction in this study.
A. reading score, because it is the response variable
B. reading score, because it is the explanatory variable
C. hours of television, because it is the response variable
D. hours of television, because it is the explanatory variable
E. it makes no difference, because there is no explanatory-response distinction in this study.
D. hours of television, because it is the explanatory variable
5
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the following table and scatter plot present data on wine consumption (in liters per person per year) and death rate from heart attacks (in deaths per 100,000 people per year) in 19 developed western countries.
use scenario 3-2. which country is represented by the clear triangle in the scatter plot?
A. new zealand
B. canada
C. finland
D. belgium
E. italy
use scenario 3-2. which country is represented by the clear triangle in the scatter plot?
A. new zealand
B. canada
C. finland
D. belgium
E. italy
B. canada
6
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the following table and scatter plot present data on wine consumption (in liters per person per year) and death rate from heart attacks (in deaths per 100,000 people per year) in 19 developed western countries.
use scenario 3-2. the correlation between wine consumption and heart disease deaths is one of the following values. from the scatterplot, which must it be?
A. r = -0.84
B. r = -0.25
C. r is very close to 0
D. r = 0.25
E. r = 0.84
use scenario 3-2. the correlation between wine consumption and heart disease deaths is one of the following values. from the scatterplot, which must it be?
A. r = -0.84
B. r = -0.25
C. r is very close to 0
D. r = 0.25
E. r = 0.84
A. r = -0.84
7
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the following table and scatter plot present data on wine consumption (in liters per person per year) and death rate from heart attacks (in deaths per 100,000 people per year) in 19 developed western countries.
use scenario 3-2. the wine consumption data are in liters of alcohol per person. which of there are all measured in liters of alcohol per person?
A. the mean, the first quartile, and the variance of wine consumption
B. the median wine consumption and correlation between wine consumption and heart disease deaths
C. the median, the variance, and the standard deviation of wine consumption
D. the standard deviation of wine consumption and the correlation between wine consumption and heart disease deaths
E. the mean, the median, and the standard deviation of wine consumption
use scenario 3-2. the wine consumption data are in liters of alcohol per person. which of there are all measured in liters of alcohol per person?
A. the mean, the first quartile, and the variance of wine consumption
B. the median wine consumption and correlation between wine consumption and heart disease deaths
C. the median, the variance, and the standard deviation of wine consumption
D. the standard deviation of wine consumption and the correlation between wine consumption and heart disease deaths
E. the mean, the median, and the standard deviation of wine consumption
E. the mean, the median, and the standard deviation of wine consumption
8
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below is a scatterplot of wine consumption (in liters per person per year) and death rate from heart attacks (in deaths per 100,000 people per year) in 19 developed western countries. european countries are designated by closed circles, other countries are designated by open circles.
which of the following statements is not supported by the information in the scatterplot?
A. about half the european countries consume more wine per person than any of the non-european countries
B. on average, the non-european countries drink less wine and have more heart attacks
C. the four countries with the highest rates of wine consumption are all european
D. the correlation between wine consumption and heart disease deaths is equally strong in european countries and non-european countries
E. the country with the highest heart disease death rate is in europe
which of the following statements is not supported by the information in the scatterplot?
A. about half the european countries consume more wine per person than any of the non-european countries
B. on average, the non-european countries drink less wine and have more heart attacks
C. the four countries with the highest rates of wine consumption are all european
D. the correlation between wine consumption and heart disease deaths is equally strong in european countries and non-european countries
E. the country with the highest heart disease death rate is in europe
D. the correlation between wine consumption and heart disease deaths is equally strong in european countries and non-european countries
9
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which of the following are most likely to be negatively correlated?
A. the total floor space and the price of an apartment in new york.
B. the percentage of body fat and the time it takes to run a mile for male college students.
C. the heights and yearly earnings of 35-year-old adults.
D. gender and yearly earnings among 35-year-old adults.
E. the prices and the weights of all racing bicycles sold last year in chicago.
A. the total floor space and the price of an apartment in new york.
B. the percentage of body fat and the time it takes to run a mile for male college students.
C. the heights and yearly earnings of 35-year-old adults.
D. gender and yearly earnings among 35-year-old adults.
E. the prices and the weights of all racing bicycles sold last year in chicago.
E. the prices and the weights of all racing bicycles sold last year in chicago
10
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consider the following scatterplot, which describes the relationship between stopping distance (in feet) and air temperature (in degrees centigrade) for a certain 2,000-pound car travelling 40 mph.
use scenario 3-3. if another data point were added with an air temperature of 0 C and a stopping distance of 80 feet, the correlation would…
A. decrease, since this new point is an outlier that does not follow the pattern in the data
B. increase, since this new point is an outlier that does not follow the pattern in the data
C. stay nearly the same, since correlation is resistant to outliers
D. increase, since there would be more data points
E. whether this data point causes an increase or decrease cannot be determined without recalculating the correlation
use scenario 3-3. if another data point were added with an air temperature of 0 C and a stopping distance of 80 feet, the correlation would…
A. decrease, since this new point is an outlier that does not follow the pattern in the data
B. increase, since this new point is an outlier that does not follow the pattern in the data
C. stay nearly the same, since correlation is resistant to outliers
D. increase, since there would be more data points
E. whether this data point causes an increase or decrease cannot be determined without recalculating the correlation
A. decrease, since this new point is an outlier that does not follow the pattern in the data
11
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which of the following is true of the correlation r?
A. it is a resistant measure of association.
B. -1 = r = 1
C. if r is the correlation between X and Y, then -r is the correlation between Y and X.
D. whenever all the data lie on a perfectly straight line, the correlation r will always be equal to +1.0
E. all of the above
A. it is a resistant measure of association.
B. -1 = r = 1
C. if r is the correlation between X and Y, then -r is the correlation between Y and X.
D. whenever all the data lie on a perfectly straight line, the correlation r will always be equal to +1.0
E. all of the above
B. -1 = r = 1
12
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which one of the following statements is correct?
A. faculty who are good researchers tend to be poor teachers and vice versa, so the correlation between teaching and research is 0.
B. women tend to be, on average, about 3.5 inches shorter than the men they marry, so the correlation between the heights of spouses must be negative
C. a researcher finds the correlation between the shoe size of children and their score on a reading test to be 0.22. the researcher must have made a mistake since these two variables are clearly unrelated and must have a correlation of 0.
D. if people with larger heads tend to be more intelligent, then we would expect the correlation between head size and intelligence to be positive.
E. the correlation r equals the proportion of times that two variables lie on a straight line.
A. faculty who are good researchers tend to be poor teachers and vice versa, so the correlation between teaching and research is 0.
B. women tend to be, on average, about 3.5 inches shorter than the men they marry, so the correlation between the heights of spouses must be negative
C. a researcher finds the correlation between the shoe size of children and their score on a reading test to be 0.22. the researcher must have made a mistake since these two variables are clearly unrelated and must have a correlation of 0.
D. if people with larger heads tend to be more intelligent, then we would expect the correlation between head size and intelligence to be positive.
E. the correlation r equals the proportion of times that two variables lie on a straight line.
D. if people with larger heads tend to be more intelligent, then we would expect the correlation between head size and intelligence to be positive
13
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consider the scatter plot below for a very small data set, consisting of the heights of five fathers (x) and their sons (y). the “M” in the plot indicated the point (x bar, y bar). the letters A - E are labels for the five father-son pairs
which father-son pair contributes the largest positive quantity to the correlation between father and son heights?
A. pair A
B. pair B
C. pair C
D. pair D
E. pair E
which father-son pair contributes the largest positive quantity to the correlation between father and son heights?
A. pair A
B. pair B
C. pair C
D. pair D
E. pair E
A. pair A
14
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consider the following scatterplot of amounts of CO (carbon monoxide) and NOX (nitrogen oxide) in grams per mile driven in the exhausts of cars. the least-squares regression line has been drawn in the plot.
use scenario 3-4. the intercept of the least-squares regression line is approximately…
A. -0.7
B. -0.1
C. 1.8
D. 2.0
E. 18.
use scenario 3-4. the intercept of the least-squares regression line is approximately…
A. -0.7
B. -0.1
C. 1.8
D. 2.0
E. 18.
C. 1.8
15
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consider the following scatterplot of amounts of CO (carbon monoxide) and NOX (nitrogen oxide) in grams per mile driven in the exhausts of cars. the least-squares regression line has been drawn in the plot.
use scenario 3-4. in the scatterplot, the point indicated by the open circle…
A. has a negative value for the residual
B. has a positive value for the residual
C. has a zero value for the residual
D. has a zero value for the correlation
E. is an outlier.
use scenario 3-4. in the scatterplot, the point indicated by the open circle…
A. has a negative value for the residual
B. has a positive value for the residual
C. has a zero value for the residual
D. has a zero value for the correlation
E. is an outlier.
A. has a negative value for the residual
16
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in a stats course, a linear regression equation was computed to predict the final exam score from the score on the first test. the equation of the least-squares regression line was y=10+0.9x where y represents the predicted final exam score and x is the score on the first exam
use scenario 3-5. suppose joe scores a 90 on the first exam. what would be the predicted value of his score on the final exam?
A. 91
B. 90
C. 89
D. 81
E. cannot be determined from the information given. we also need to know the correlation.
use scenario 3-5. suppose joe scores a 90 on the first exam. what would be the predicted value of his score on the final exam?
A. 91
B. 90
C. 89
D. 81
E. cannot be determined from the information given. we also need to know the correlation.
A. 91
17
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which of the following statements are true about the least-squares regression line?
i. the slope is the predicted change in the response variable associated with a unit increase in the explanatory variable
ii. the line always passes through the point (j, m), the means of the explanatory and response variables, respectively
iii. it is the line that minimizes the sum of the squared residuals
A. i only
B. ii only
C. iii only
D. i and iii only
E. i, ii, and iii are all true.
i. the slope is the predicted change in the response variable associated with a unit increase in the explanatory variable
ii. the line always passes through the point (j, m), the means of the explanatory and response variables, respectively
iii. it is the line that minimizes the sum of the squared residuals
A. i only
B. ii only
C. iii only
D. i and iii only
E. i, ii, and iii are all true.
E. i, ii, and iii are all true
18
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use scenario 3-6. the y-intercept of the least-squares line is…
A. -10.95
B. 4.52
C. 4.65
D. 8.48
E. 8.55
A. -10.95
B. 4.52
C. 4.65
D. 8.48
E. 8.55
C. 4.65
19
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the correlation between the age and height of children is found to be about r = 0.7. suppose we use the age x of a child to predict the height y of the child. we conclude that…
A. the least-squares regression line of y on x would have a slope of 0.7.
B. the fraction of the variation in heights explained by the least-squares regression line of y on x is 0.49
C. about 70% of the time, age will accurately predict height.
D. the fraction of the variation in heights explained by the least-squares regression line of y on x is 0.70.
E. the line explains about 49% of the data
A. the least-squares regression line of y on x would have a slope of 0.7.
B. the fraction of the variation in heights explained by the least-squares regression line of y on x is 0.49
C. about 70% of the time, age will accurately predict height.
D. the fraction of the variation in heights explained by the least-squares regression line of y on x is 0.70.
E. the line explains about 49% of the data
B. the fraction of the variation in heights explained by the least-squares regression line of y on x is 0.49
20
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suppose we fit the least-squares regression line to a set of data. if a plot of the residuals shows a curved pattern,
A. a straight line is not a good summary for the data
B. the correlation must be 0
C. the correlation must be positive.
D. outliers must be present.
E. r2 = 0
A. a straight line is not a good summary for the data
B. the correlation must be 0
C. the correlation must be positive.
D. outliers must be present.
E. r2 = 0
A. a straight line is not a good summary for the data
21
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which of the following statements about influential points and outliers is true?
i. an influential point always has a high residual
ii. outliers are always influential points.
iii. removing an influential point always causes a marked change in either the correlation, the regression equation, or both
.A. i only
B. ii only
C. iii only
D. ii and iii only
E. i, ii, and iii are all true
i. an influential point always has a high residual
ii. outliers are always influential points.
iii. removing an influential point always causes a marked change in either the correlation, the regression equation, or both
.A. i only
B. ii only
C. iii only
D. ii and iii only
E. i, ii, and iii are all true
C. iii only
22
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BEANS
use scenario 3-7. which of the following statements is a correct interpretation of the slope of the regression line?
A. for each 1 unit increase in the calorie content, the predicted protein content increases bt 2.08 grams
B. for each 1 unit increase in the calorie content, the predicted protein content increases by 2.08 grams
C. for each 1 gram increase in the protein content, the predicted calorie content increases by 2.08 grams
D. for each 1 gram increase in the protein content, the predicted calorie content increases by 0.063 grams
E. for each 1 gram increase in the protein content, the predicted calorie content increases by 0.024 grams
use scenario 3-7. which of the following statements is a correct interpretation of the slope of the regression line?
A. for each 1 unit increase in the calorie content, the predicted protein content increases bt 2.08 grams
B. for each 1 unit increase in the calorie content, the predicted protein content increases by 2.08 grams
C. for each 1 gram increase in the protein content, the predicted calorie content increases by 2.08 grams
D. for each 1 gram increase in the protein content, the predicted calorie content increases by 0.063 grams
E. for each 1 gram increase in the protein content, the predicted calorie content increases by 0.024 grams
B. for each 1 unit increase in the calorie content, the predicted protein content increases by 2.08 grams
23
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BEANS
use scenario 3-7. the circled point on the scatter plot represents lima beans, which have 621 calories and 37 grams of protein. the residual for lima beans is…
A. -37.0
B. -4.18
C. 4.18
D. 37.0
E. 41.18
use scenario 3-7. the circled point on the scatter plot represents lima beans, which have 621 calories and 37 grams of protein. the residual for lima beans is…
A. -37.0
B. -4.18
C. 4.18
D. 37.0
E. 41.18
B. -4.18
24
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the least-squares regression line is fit to a set of data. if one of the data points has a positive residual, then…
A. the correlation between the values of the response and explanatory variables must be positive
B. the point must lie above the least-squares regression line
C. the point must lie near the right edge of the scatterplot
D. the point is probably an influential point
E. all of the above
A. the correlation between the values of the response and explanatory variables must be positive
B. the point must lie above the least-squares regression line
C. the point must lie near the right edge of the scatterplot
D. the point is probably an influential point
E. all of the above
B. the point must lie above the least-squares regression line
25
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a study of child development measures the age (in months) at which a child begins to talk and also the child's score on an ability test given several years later. the study asks whether the age at which a child talks helps predict the later test score. the least-squares regression line of test score y on age x is y = 110 - 1.3x. according to this regression line, what happens (on the average) to children who talk one month later than other children?
A. their predicted test scores go down 110 points.
B. their predicted test scores go down 1.3 points
C. their predicted test scores go up 110 points.
D. their predicted test scores go up 1.3 points
E. their predicted test scores are 108.7
A. their predicted test scores go down 110 points.
B. their predicted test scores go down 1.3 points
C. their predicted test scores go up 110 points.
D. their predicted test scores go up 1.3 points
E. their predicted test scores are 108.7
B. their predicted test scores go down 1.3 points
26
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fishy table
use scenario 3-8. on average, how far are the predicted y-values from the actual y-values?
A. 25.55
B. 5.392
C. 6.75133
D. 0.687
E. cannot be determined without the original data
use scenario 3-8. on average, how far are the predicted y-values from the actual y-values?
A. 25.55
B. 5.392
C. 6.75133
D. 0.687
E. cannot be determined without the original data
C. 6.75133
27
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use scenario 3-8. which of the following us the plot of residuals versus fish lengths. (all of the options are different scatterplots)
D.
28
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a study gathers data on the outside temperature during the winter, in degrees fahrenheit, and the amount of natural gas a household consumes, in cubic feet per day. call the temperature x, and gas consumption y. the house is heated with gas, so x helps explain y. the least-squares regression line for predicting y from x is: y=1344-19x
use scenario 3-9. on a day when the temperature is 20 F, the regression line predicts that gas used will be about…
A. 1724 cubic feet.
B. 1383 cubic feet.
C. 1325 cubic feet.
D. 964 cubic feet.
E. none of the above
use scenario 3-9. on a day when the temperature is 20 F, the regression line predicts that gas used will be about…
A. 1724 cubic feet.
B. 1383 cubic feet.
C. 1325 cubic feet.
D. 964 cubic feet.
E. none of the above
D. 964 cubic feet
29
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a study gathers data on the outside temperature during the winter, in degrees fahrenheit, and the amount of natural gas a household consumes, in cubic feet per day. call the temperature x, and gas consumption y. the house is heated with gas, so x helps explain y. the least-squares regression line for predicting y from x is: y=1344-19x
use scenario 3-9. what does the number 1344 represent in the equation?
A. predicted gas usage (in cubic feet) when the temperature is 19 degrees fahrenheit
B. predicted gas usage (in cubic feet) when the temperature is 0 degrees fahrenheit
C. it's the y-intercept of the regression line, but it has no practical purpose in the context of the problem
D. the maximum possible gas a household can use
E. none of the above
use scenario 3-9. what does the number 1344 represent in the equation?
A. predicted gas usage (in cubic feet) when the temperature is 19 degrees fahrenheit
B. predicted gas usage (in cubic feet) when the temperature is 0 degrees fahrenheit
C. it's the y-intercept of the regression line, but it has no practical purpose in the context of the problem
D. the maximum possible gas a household can use
E. none of the above
B. predicted gas usage (in cubic feet) when the temperature is 0 degrees fahrenheit
30
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scores on the 1995 SAT verbal aptitude test x among kentucky high school seniors were normally distributed with a mean 420 and a standard deviation of 80. scores on the 1995 SAT quantitative aptitude test y among kentucky high school seniors were normally distributed with a mean 440 and standard deviation 60. the least-squares regression line has the equation y = 0.6x + 188. the correlation between verbal scores and math scores is…
A. -0.8
B. 0
C. 0.45
D. 0.8
E. cannot be determined from the information given
A. -0.8
B. 0
C. 0.45
D. 0.8
E. cannot be determined from the information given
D. 0.8
31
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which of the following statements describes what the standard deviation of residuals for a regression equation can be used for?
i. it describes the typical vertical distance between an observed data point and the regression line
ii. it evaluates whether a linear model is appropriate for a set of data
iii. it measures the overall precision of predictions made using the regression equation.
A. i only
B. ii only
C. iii only
D. both i and ii
E. both i and iii
i. it describes the typical vertical distance between an observed data point and the regression line
ii. it evaluates whether a linear model is appropriate for a set of data
iii. it measures the overall precision of predictions made using the regression equation.
A. i only
B. ii only
C. iii only
D. both i and ii
E. both i and iii
E. both i and iii