Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Provide an appropriate response.
1)
In the context of regression analysis, which of the following, roughly speaking , does the standard
error of the estimate give an indication of?
1)
A)
How much the slope of the sample regression line differs from the slope of the population
regression line.
B)
How much, on average, the values of the response variable differ from their mean.
C)
How much, on average, the predicted values of the response variable differ from the observed
values of the response variable.
D)
How much, on average, the values of the predictor variable differ from their mean.
2)
In a study of the relationship between weight and height, a sample regression equation is obtained,
in which height is used as the predictor variable. This sample regression equation is then used to
make inferences. Which of the following statements is true?
2)
A)
A 95% confidence interval for the mean weight of all subjects of height 65 inches will be the
same width as a 95% prediction interval for the weight of an individual of height 65 inches.
B)
A 95% confidence interval for the mean weight of all subjects of height 65 inches will be
narrower than a 95% prediction interval for the weight of an individual of height 65 inches.
C)
A 95% confidence interval for the mean weight of all subjects of height 65 inches will be wider
than a 95% prediction interval for the weight of an individual of height 65 inches.
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Paired sample data is given. Discuss what it would mean for Assumptions 1–3 for regression inferences to be satisfied by
the variables under consideration.
3)
A social scientist is interested in the relationship between age and income in adults aged
20–60. A random sample of eight adults yields the following data, where x denotes age in
years and y denotes annual income in thousands of dollars.
x27 55 48 25 31 44 57 35
y 18.9 48.3 27.6 33.2 19.6 65.0 55.6 20.1
3)
Construct a residual plot for the given data.
4)
^
x 2 4 5 6
y 7 11 13 20 y= 3x
4)
Decide, at the given significance level, whether the data provide sufficient evidence to conclude that x is useful for
predicting y.
5)
^
The sample data below are the typing speeds (in words per minute) and reading speeds (in
words per minute) of nine randomly selected secretaries. Here, x denotes typing speed,
and y denotes reading
speed.
x 60 56 52 63 70 58 44 79 62
y 370 551 528 348 645 454 503 618 500 y= 290.2 + 3.502x
The standard error of the estimate is approximately 100.33479. At the 10% level of
significance, do the data provide sufficient evidence to conclude that the slope of the
population regression line is not 0 and hence that typing speed is useful as a predictor of
reading speed?
5)
Paired sample data is given. Discuss what it would mean for Assumptions 1–3 for regression inferences to be satisfied by
the variables under consideration.
6)
A researcher is interested in the relationship between height and foot length for female
adults. A random sample of nine women yields the following data, where x denotes height
in inches and y denotes foot length in inches.
x61 64 60 64 67 65 62 69 62
y 8.9 9.4 9.0 9.2 10.0 9.7 9.1 10.3 9.5
6)
Provide an appropriate response.
7)
In the context of linear correlation, explain the difference between r and .
7)
Construct a normal probability plot of the residuals for the given regression data.
8)
^
x 0 1 5 3 3
y 7 5 –4 0 1 y= 7.105 – 2.211x
8)
Provide an appropriate response.
9)
The graph below is a normal probability plot for the residuals for a set of regression data.
Does the graph suggest violation of one or more of the assumptions for regression
inferences? Explain your answer.
9)
Construct a residual plot for the given data.
10)
^
Applicants for a particular job, which involves extensive travel in Spanish speaking
countries, must take a proficiency test in Spanish. The sample data below were obtained in
a study of the relationship between the numbers of years applicants have studied Spanish
(x) and their score on the test (y).
x 3 4 4 2 5 3 4 5 3 2
y 57 78 72 58 89 63 73 84 75 48 y= 31.55 + 10.90x
10)
Provide an appropriate response.
11)
In the context of regression analysis, explain what is meant by the term “residual”.
11)
12)
^
Applicants for a particular job, which involves extensive travel in Spanish speaking
countries, must take a proficiency test in Spanish. The sample data below were obtained in
a study of the relationship between the numbers of years applicants have studied Spanish
(x) and their score on the test (y).
x 3 4 4 2 5 3 4 5 3 2
y 57 78 72 58 89 63 73 84 75 48 y= 31.55 + 10.90x
A 99% confidence interval for the slope of the population regression line that relates test
score to number of years of study is 5.05 to 16.75. Provide an interpretation of this
confidence interval.
12)
13)
The graph below is a residual plot for a set of regression data. Does the graph suggest
violation of one or more of the assumptions for regression inferences? Explain your
answer.
13)
Perform the required correlation test. You may presume that the assumptions for regression inferences are met.
14)
Decide, at the 10% significance level, whether the data provide sufficient evidence to reject
the null hypothesis in favor of the alternative hypothesis.
x 3 2 4
y 8 4 6 Ha: > 0
14)
Construct a normal probability plot of the residuals for the given regression data.
15)
^
A grass seed company conducts a study to determine the relationship between the density
of seeds planted (in pounds per 500 sq ft) and the quality of the resulting lawn. Eight
similar plots of land are selected and each is planted with a particular density of seed. One
month later the quality of each lawn is rated on a scale of 0 to 100. The sample data are
given below, where x denotes seed density, and y denotes lawn quality.
x 1 1 2 3 3 3 4 5
y 30 40 40 40 50 65 50 50 y= 33.14 + 4.54x
15)
Provide an appropriate response.
16)
Is it possible for a sample linear correlation coefficient, r, to be close to 0 even though the
population correlation coefficient, , is close to 1? Explain your answer.
16)
Perform the required correlation test. You may presume that the assumptions for regression inferences are met.
17)
The sample data below are the typing speeds (in words per minute) and reading speeds (in
words per minute) of nine randomly selected secretaries. Here, x denotes typing speed,
and y denotes reading speed.
x 60 56 52 63 70 58 44 79 62
y 370 551 528 348 645 454 503 618 500
The sample linear correlation coefficient is r = 0.352. At the 10% significance level, do the
data provide sufficient evidence to conclude that typing speed and reading speed are
linearly correlated?
17)
18)
A set of sample data consisting of 19 pairs of x and y values yields a sample linear
correlation coefficient of –0.633. At the 1% significance level, do the data provide sufficient
evidence to conclude that x and y are negatively linearly correlated?
18)
Construct a residual plot for the given data.
19)
^
A grass seed company conducts a study to determine the relationship between the density
of seeds planted (in pounds per 500 sq ft) and the quality of the resulting lawn. Eight
similar plots of land are selected and each is planted with a particular density of seed. One
month later the quality of each lawn is rated on a scale of 0 to 100. The sample data are
given below, where x denotes seed density, and y denotes lawn quality.
x 1 1 2 3 3 3 4 5
y 30 40 40 40 50 65 50 50 y= 33.14 + 4.54x
19)
Perform the required correlation test. You may presume that the assumptions for regression inferences are met.
20)
Decide, at the 10% significance level, whether the data provide sufficient evidence to reject
the null hypothesis in favor of the alternative hypothesis.
x 0 1 5 3 3
y 7 5 –4 0 1 Ha: 0
20)
Decide, at the given significance level, whether the data provide sufficient evidence to conclude that x is useful for
predicting y.
21)
^
Ten students in a graduate program were randomly selected. Their grade point averages
(GPAs) when they entered the program were between 3.5 and 4.0. The following data
consist of the students’ GPAs (x) on entering the program and their current GPAs (y).
x 3.5 3.8 3.6 3.6 3.5 3.9 4.0 3.9 3.5 3.7
y 3.6 3.7 3.9 3.6 3.9 3.8 3.7 3.9 3.8 4.0 y= 3.67 + 0.0313x
The standard error of the estimate is approximately 0.14521. At the 10% level of
significance, do the data provide sufficient evidence to conclude that the slope of the
population regression line is not 0 and hence that entering GPA is useful as a predictor of
current GPA?
21)
Perform the required correlation test. You may presume that the assumptions for regression inferences are met.
22)
A set of sample data consisting of 16 pairs of x and y values yields a sample linear
correlation coefficient of –0.347. At the 2.5% significance level, do the data provide
sufficient evidence to conclude that x and y are negatively linearly correlated?
22)
Decide, at the given significance level, whether the data provide sufficient evidence to conclude that x is useful for
predicting y.
23)
^
Decide, at the 10% significance level, whether the data provide sufficient evidence to
conclude that x is a useful predictor of y.
x 3 2 4
y 8 4 6 y= 3 + x
23)
Construct a residual plot for the given data.
24)
^
x 0 1 5 3 3
y 7 5 –4 0 1 y= 7.105 – 2.211x
24)
Paired sample data is given. Discuss what it would mean for Assumptions 1–3 for regression inferences to be satisfied by
the variables under consideration.
25)
A social scientist is interested in the relationship between years of education and income in
adults in the U.S. A random sample of nine working adults yields the following data,
where x denotes years of education completed and y denotes annual income in thousands
of dollars.
x10 11 17 15 14 12 11 11 15
y 20.5 17.4 54.8 44.2 33.9 66.2 19.3 34.5 32.8
25)
11
Decide, at the given significance level, whether the data provide sufficient evidence to conclude that x is useful for
predicting y.
26)
^
Applicants for a particular job, which involves extensive travel in Spanish speaking
countries, must take a proficiency test in Spanish. The sample data below were obtained in
a study of the relationship between the numbers of years applicants have studied Spanish
(x) and their score on the test (y).
x 3 4 4 2 5 3 4 5 3 2
y 57 78 72 58 89 63 73 84 75 48 y= 31.55 + 10.90x
The standard error of the estimate is approximately 5.651. At the 5% level of significance,
do the data provide sufficient evidence to conclude that the slope of the population
regression line is not 0 and hence that number of years of study is useful as a predictor of
score on the test?
26)
27)
^
A grass seed company conducts a study to determine the relationship between the density
of seeds planted (in pounds per 500 sq ft) and the quality of the resulting lawn. Eight
similar plots of land are selected and each is planted with a particular density of seed. One
month later the quality of each lawn is rated on a scale of 0 to 100. The sample data are
given below, where x denotes seed density, and y denotes lawn quality.
x 1 1 2 3 3 3 4 5
y 30 40 40 40 50 65 50 50 y= 33.14 + 4.54x
The standard error of the estimate is approximately 9.074. At the 1% level of significance,
do the data provide sufficient evidence to conclude that the slope of the population
regression line is not 0 and hence that seed density is useful as a predictor of lawn quality?
27)
Construct a residual plot for the given data.
28)
^
x 3 2 4
y 8 4 6 y= 3 + x
28)
Paired sample data is given. Discuss what it would mean for Assumptions 1–3 for regression inferences to be satisfied by
the variables under consideration.
29)
A physiologist is interested in the relationship between age and blood pressure in adults in
the U.S. A random sample of eight adults yields the following data, where x denotes age in
years and y denotes systolic blood pressure in mm Hg.
x27 55 48 75 31 44 67 35
y 118 133 127 143 120 126 133 116
29)
13
Perform the required correlation test. You may presume that the assumptions for regression inferences are met.
30)
Ten students in a graduate program were randomly selected. Their grade point averages
(GPAs) when they entered the program were between 3.5 and 4.0. The following data
consist of the students’ GPAs (x) on entering the program and their current GPAs (y).
x 3.5 3.8 3.6 3.6 3.5 3.9 4.0 3.9 3.5 3.7
y 3.6 3.7 3.9 3.6 3.9 3.8 3.7 3.9 3.8 4.0
The sample linear correlation coefficient is r = 0.043. At the 5% significance level, do the
data provide sufficient evidence to conclude that entering GPA and current GPA are
linearly correlated?
30)
Decide, at the given significance level, whether the data provide sufficient evidence to conclude that x is useful for
predicting y.
31)
^
The sample data below are the index of exposure (x) to radioactive waste for nine different
Oregon counties and cancer mortality rate (y) (deaths per 100,000).
x 2.49 2.57 3.41 1.25 1.62 3.83 11.64 6.41 8.34
y 147.1 130.1 129.9 113.5 137.5 162.3 207.5 177.9 210.3 y= 114.72 + 9.23x
The standard error of the estimate is approximately 14.0099. At the 5% level of
significance, do the data provide sufficient evidence to conclude that the slope of the
population regression line is not 0 and hence that index of exposure is useful as a predictor
of cancer mortality rate?
31)
Provide an appropriate response.
32)
In a study of the relationship between height and weight, a sample regression equation is
obtained in which height is used as the predictor variable. Explain why a confidence
interval for a conditional mean corresponding to the height 70 inches is narrower than a
prediction interval corresponding to the height 70 inches.
32)
33)
If the assumptions for regression inferences are met, what would you expect to see when
constructing a residual plot and a normal probability plot for the residuals?
33)
Decide, at the given significance level, whether the data provide sufficient evidence to conclude that x is useful for
predicting y.
34)
^
Decide, at the 10% significance level, whether the data provide sufficient evidence to
conclude that x is a useful predictor of y.
x 2 4 5 6
y 7 11 13 20 y= 3x
34)
Perform the required correlation test. You may presume that the assumptions for regression inferences are met.
35)
A grass seed company conducts a study to determine the relationship between the density
of seeds planted (in pounds per 500 sq ft) and the quality of the resulting lawn. Eight
similar plots of land are selected and each is planted with a particular density of seed. One
month later the quality of each lawn is rated on a scale of 0 to 100. The sample data are
given below, where x denotes seed density, and y denotes lawn quality.
x 1 1 2 3 3 3 4 5
y 30 40 40 40 50 65 50 50
The sample linear correlation coefficient is r = 0.600. At the 1% significance level, do the
data provide sufficient evidence to conclude that seed density and lawn quality are
positively linearly correlated?
35)
Construct a normal probability plot of the residuals for the given regression data.
36)
^
x 2 4 5 6
y 7 11 13 20 y= 3x
36)
37)
^
x 3 2 4
y 8 4 6 y= 3 + x
37)
Provide an appropriate response.
38)
^
The sample data below are the index of exposure (x) to radioactive waste for nine different
Oregon counties and cancer mortality rate (y) (deaths per 100,000).
x 2.49 2.57 3.41 1.25 1.62 3.83 11.64 6.41 8.34
y 147.1 130.1 129.9 113.5 137.5 162.3 207.5 177.9 210.3 y= 114.72 + 9.23x
A 99% confidence interval for the slope of the population regression line that relates cancer
mortality rate to index of exposure is 4.26 to 14.20. Provide an interpretation of this
confidence interval.
38)
Perform the required correlation test. You may presume that the assumptions for regression inferences are met.
39)
The sample data below are the index of exposure (x) to radioactive waste for nine different
Oregon counties and cancer mortality rate (y) (deaths per 100,000).
x 2.49 2.57 3.41 1.25 1.62 3.83 11.64 6.41 8.34
y 147.1 130.1 129.9 113.5 137.5 162.3 207.5 177.9 210.3
The sample linear correlation coefficient is r = 0.926. At the 5% significance level, do the
data provide sufficient evidence to conclude that index of exposure and cancer mortality
rate are linearly correlated?
39)
40)
A set of sample data consisting of 23 pairs of x and y values yields a sample linear
correlation coefficient of 0.776. At the 1% significance level, do the data provide sufficient
evidence to conclude that x and y are linearly correlated?
40)
41)
Applicants for a particular job, which involves extensive travel in Spanish speaking
countries, must take a proficiency test in Spanish. The sample data below were obtained in
a study of the relationship between the numbers of years applicants have studied Spanish
(x) and their score on the test (y).
x 3 4 4 2 5 3 4 5 3 2
y 57 78 72 58 89 63 73 84 75 48
The sample linear correlation coefficient is r = 0.911. At the 5% significance level, do the
data provide sufficient evidence to conclude that number of years of study and test score
are positively linearly correlated?
41)
Construct a normal probability plot of the residuals for the given regression data.
18
42)
^
Applicants for a particular job, which involves extensive travel in Spanish speaking
countries, must take a proficiency test in Spanish. The sample data below were obtained in
a study of the relationship between the numbers of years applicants have studied Spanish
(x) and their score on the test (y).
x 3 4 4 2 5 3 4 5 3 2
y 57 78 72 58 89 63 73 84 75 48 y= 31.55 + 10.90x
42)
Provide an appropriate response.
43)
When testing to determine if correlation is significant, we use the hypotheses H0: = 0.
Ha: 0. Suppose the conclusion is to reject the null hypothesis. What does that tell us
about the linear regression equation?
43)
44)
A researcher is interested in the relationship between age and income. He performs a
regression analysis using age as the predictor variable and annual income as the response
variable. He obtains the equation of the regression line and then computes the standard
error of the estimate, which comes out to $6570. Give an interpretation of the standard
error of the estimate.
44)
Decide, at the given significance level, whether the data provide sufficient evidence to conclude that x is useful for
predicting y.
45)
^
Decide, at the 10% significance level, whether the data provide sufficient evidence to
conclude that x is a useful predictor of y.
x 0 1 5 3 3
y 7 5 –4 0 1 y= 7.105 – 2.211x
45)
Construct a residual plot for the given data.
46)
^
The sample data below are the typing speeds (in words per minute) and reading speeds
(in words per minute) of nine randomly selected secretaries. Here, x denotes typing speed,
and y denotes reading
speed.
x 60 56 52 63 70 58 44 79 62
y 370 551 528 348 645 454 503 618 500 y= 290.2 + 3.502x
46)
Provide an appropriate response.
47)
The graph below is a residual plot for a set of regression data. Does the graph suggest
violation of one or more of the assumptions for regression inferences? Explain your
answer.
47)
48)
In the context of regression, explain the difference between a confidence interval for a
conditional mean and a prediction interval.
48)
Construct a normal probability plot of the residuals for the given regression data.
49)
^
The sample data below are the typing speeds (in words per minute) and reading speeds
(in words per minute) of nine randomly selected secretaries. Here, x denotes typing speed,
and y denotes reading
speed.
x 60 56 52 63 70 58 44 79 62
y 370 551 528 348 645 454 503 618 500 y= 290.2 + 3.502x
49)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Provide an appropriate response.
50)
In a study of the relationship between weight and height, a sample regression equation is obtained,
in which height is used as the predictor variable. This sample regression equation is then used to
make inferences. Is it true or false that the point estimate of the mean weight of all subjects of
height 65 inches will be equal to the predicted weight of an individual of height 65 inches.?
50)
A)
True
B)
False
Obtain the required confidence interval for the conditional mean. You may presume that the assumptions for regression
inferences are met.
51)
^
Find a 95% confidence interval for the conditional mean of the response variable at x =6.
x 2 4 5 6
y 7 11 13 20 y= 3x
51)
A)
12.547 to 27.453
B)
12.489 to 23.511
C)
12.942 to 23.058
D)
10.547 to 25.453
52)
^
Find a 95% confidence interval for the conditional mean of the response variable at x =4.
x 3 2 4
y 8 4 6 y= 3 + x
52)
A)
–21.412 to 35.412
B)
–2.622 to 16.622
C)
–7.119 to 21.119
D)
31.412 to 37.412
Obtain the required point estimate of the mean or predicted y–value. You may presume that the assumptions for
regression inferences are met and that x is useful as a predictor of y.
53)
^
The sample data below are the index of exposure (x) to radioactive waste for nine different Oregon
counties and cancer mortality rate (y) (deaths per 100,000).
x 2.49 2.57 3.41 1.25 1.62 3.83 11.64 6.41 8.34
y 147.1 130.1 129.9 113.5 137.5 162.3 207.5 177.9 210.3 y= 114.72 + 9.23x
Use the data to predict the cancer mortality rate for a county whose index of exposure is 8.97.
Round your answer to one decimal place.
53)
A)
194.6 deaths per 100,000
B)
197.5 deaths per 100,000
C)
132.9 deaths per 100,000
D)
201.7 deaths per 100,000
54)
^
A grass seed company conducts a study to determine the relationship between the density of seeds
planted (in pounds per 500 sq ft) and the quality of the resulting lawn. Eight similar plots of land
are selected and each is planted with a particular density of seed. One month later the quality of
each lawn is rated on a scale of 0 to 100. The sample data are given below, where x denotes seed
density, and y denotes lawn quality.
x 1 1 2 3 3 3 4 5
y 30 40 40 40 50 65 50 50 y= 33.14 + 4.54x
Round your answer to two decimal places.
54)
A)
40.08
B)
35.54
C)
44.04
D)
45.14
D)
Obtain the required prediction interval. You may presume that the assumptions for regression inferences are met.
55)
^
Find a 95% prediction interval for the value of the response variable at x =3.
x 0 1 5 3 3
y 7 5 –4 0 1 y= 7.105 – 2.211x
55)
A)
–1.003 to 1.947
B)
–0.475 to 2.475
C)
–0.618 to 1.562
D)
–0.814 to 1.758
D)
Provide an appropriate response.
56)
The table below gives the career free–throw percentage and the player height for a sample of NBA
basketball players, both past and present. Assuming that there is a relationship between height and
free–throw percentage, use Minitab to find a 95% prediction interval for the mean free–throw
percentage of Kevin Garnett, who is 2.00 meters tall.
Height (meters) Career Free–throw %
1.83
2.16
2.13
2.26
2.11
2.01
1.83
1.98
76.0
54.2
71.0
81.1
75.6
78.2
90.4
82.1
Height (meters) Career Free–throw %
2.18
2.08
2.01
1.60
2.06
2.03
2.21
2.29
72.1
69.2
58.4
82.7
88.6
84.8
64.9
56.1
56)
A)
75.50% to 77.10%
B)
70.00% to 81.20%
C)
53.33% to 97.90%
D)
69.75% to 81.35%
D)
57)
The table below gives the career free–throw percentage and the player height for a sample of NBA
basketball players, both past and present. Assuming that the data can be modeled with a linear
model, use technology to obtain the standard error of the estimate.
Height (meters) Career Free–throw %
1.83
2.16
2.13
2.26
2.11
2.01
1.83
1.98
76.0
54.2
71.0
81.1
75.6
78.2
90.4
82.1
Height (meters) Career Free–throw %
2.18
2.08
2.01
1.60
2.06
2.03
2.21
2.29
72.1
69.2
58.4
82.7
88.6
84.8
64.9
56.1
57)
A)
9.3804
B)
2.7970
C)
2.9901
D)
10.0280
Obtain the required confidence interval for the conditional mean. You may presume that the assumptions for regression
inferences are met.
58)
^
Applicants for a particular job, which involves extensive travel in Spanish speaking countries,
must take a proficiency test in Spanish. The sample data below were obtained in a study of the
relationship between the numbers of years applicants have studied Spanish (x) and their score on
the test (y).
x 3 4 4 2 5 3 4 5 3 2
y 57 78 72 58 89 63 73 84 75 48 y= 31.55 + 10.90x
The standard error of the estimate is se= 5.651. Determine a 95% confidence interval for the mean
score of all applicants who have studied Spanish for 3.7 years.
58)
A)
58.2 to 85.6
B)
67.8 to 76.0
C)
67.7 to 76.1
D)
68.5 to 75.3
59)
^
Find a 95% confidence interval for the conditional mean of the response variable at x =1.
x 0 1 5 3 3
y 7 5 –4 0 1 y= 7.105 – 2.211x
59)
A)
4.13 to 5.658
B)
4.236 to 5.764
C)
4.329 to 5.459
D)
4.227 to 5.561
Provide an appropriate response.
26
60)
The following table gives the US domestic oil production rates (excluding Alaska) over the past few
years. Assuming that the data can be modeled with a linear model, use technology to obtain a
residual plot and a normal probability plot of the residuals.
Year Millions of barrels per day
1987 6.39
1988 6.12
1989 5.74
1990 5.58
1991 5.62
1992 5.46
1993 5.26
1994 5.10
Year Millions of barrels per day
1995 5.08
1996 5.07
1997 5.16
1998 5.08
1999 4.83
2000 4.85
2001 4.84
2002 4.83
60)
A)
Residuals: Normal Probability Plot:
B)
Residuals: Normal Probability Plot:
C)
Residuals: Normal Probability Plot:
D)
Residuals: Normal Probability Plot:
C)
D)
Obtain the required confidence interval for the conditional mean. You may presume that the assumptions for regression
inferences are met.
61)
^
The sample data below are the typing speeds (in words per minute) and reading speeds (in words
per minute) of nine randomly selected secretaries. Here, x denotes typing speed, and y denotes
reading
speed.
x 60 56 52 63 70 58 44 79 62
y 370 551 528 348 645 454 503 618 500 y= 290.2 + 3.502x
The standard error of the estimate is se= 100.33479. Determine a 90% confidence interval for the
mean reading speed of all secretaries whose typing speed is 66.
61)
A)
449.3 to 593.4 words per minute
B)
466.5 to 576.2 words per minute
C)
317.5 to 725.1 words per minute
D)
447.9 to 594.8 words per minute
Provide an appropriate response.
62)
^
A grass seed company conducts a study to determine the relationship between the density of seeds
planted (in pounds per 500 sq ft) and the quality of the resulting lawn. Eight similar plots of land
are selected and each is planted with a particular density of seed. One month later the quality of
each lawn is rated on a scale of 0 to 100. The sample data are given below, where x denotes seed
density, and y denotes lawn quality.
x 1 1 2 3 3 3 4 5
y 30 40 40 40 50 65 50 50 y= 33.14 + 4.54x
A 95% confidence interval for the slope of the population regression line that relates lawn quality to
seed density is –1.50 to 10.58. Which of the following is a correct interpretation of this confidence
interval? There may be more than one correct interpretation.
A: We can be 95% confident that the slope, 1, of the population regression line is between –1.50
and 10.58.
B: We can be 95% confident that with each unit increase in seed density, the increase in lawn
quality is somewhere between –1.50 and 10.58.
C: We can be 95% confident that with each unit increase in seed density, the increase in mean lawn
quality is somewhere between –1.50 and 10.58.
D: If seed density increases by one unit, there is a 95% chance that the increase in lawn quality lies
between –1.50 and 10.58.
62)
A)
A and B
B)
A, C, and D
C)
B and C
D)
A and C
C)
D)
C)
D)
Obtain the required confidence interval for the slope of the population regression line. You may presume that the
assumptions for regression inferences are met.
63)
^
Find a 90% confidence interval for the slope of the population regression line.
x 3 2 4
y 8 4 6 y= 3 + x
63)
A)
–4.331 to 6.331
B)
–4.058 to 6.058
C)
–6.733 to 8.733
D)
–9.936 to 11.936
Provide an appropriate response.
64)
The table below gives the career free–throw percentage and the player height for a sample of NBA
basketball players, both past and present. Use technology to compute a p–value and use it to
determine whether the regression equation is useful for making predictions about freethrow
percentage. Test at the 10% significance level with the hypotheses H0: 1= 0 and Ha: 1
0.
Height (meters) Career Free–throw %
1.83
2.16
2.13
2.26
2.11
2.01
1.83
1.98
76.0
54.2
71.0
81.1
75.6
78.2
90.4
82.1
Height (meters) Career Free–throw %
2.18
2.08
2.01
1.60
2.06
2.03
2.21
2.29
72.1
69.2
58.4
82.7
88.6
84.8
64.9
56.1
64)
A)
p = 0.02311. Since p <, reject the null hypothesis. The regression equation is useful for
making free throw percentage predictions.
B)
p = 0.04622. Since p <, reject the null hypothesis. The regression equation is useful for
making free throw percentage predictions.
C)
p = 0.04622. Since p <, do not reject the null hypothesis. The regression equation is not
useful for making free throw percentage predictions.
D)
p = 0.02311. Since p <, do not reject the null hypothesis. The regression equation is not
useful for making free throw percentage predictions.
65)
The table below gives the career free–throw percentage and the player height for a sample of NBA
basketball players, both past and present. Assuming that the data can be modeled with a linear
model, use technology to obtain a normal probability plot of the residuals.
Height (meters) Career Free–throw %
1.83
2.16
2.13
2.26
2.11
2.01
1.83
1.98
76.0
54.2
71.0
81.1
75.6
78.2
90.4
82.1
Height (meters) Career Free–throw %
2.18
2.08
2.01
1.60
2.06
2.03
2.21
2.29
72.1
69.2
58.4
82.7
88.6
84.8
64.9
56.1
65)
A)
B)
C)
30
D)
66)
The table below gives the career free–throw percentage and the player height for a sample of NBA
basketball players, both past and present. Assuming that the data can be modeled with a linear
model, use technology to obtain a residual plot.
Height (meters) Career Free–throw %
1.83
2.16
2.13
2.26
2.11
2.01
1.83
1.98
76.0
54.2
71.0
81.1
75.6
78.2
90.4
82.1
Height (meters) Career Free–throw %
2.18
2.08
2.01
1.60
2.06
2.03
2.21
2.29
72.1
69.2
58.4
82.7
88.6
84.8
64.9
56.1
66)
A)
31
B)
C)
D)
Obtain the required confidence interval for the slope of the population regression line. You may presume that the
assumptions for regression inferences are met.
67)
^
The sample data below are the index of exposure (x) to radioactive waste for nine different Oregon
counties and cancer mortality rate (y) (deaths per 100,000).
x 2.49 2.57 3.41 1.25 1.62 3.83 11.64 6.41 8.34
y 147.1 130.1 129.9 113.5 137.5 162.3 207.5 177.9 210.3 y= 114.72 + 9.23x
The standard error of the estimate is approximately 14.0099. Find a 99% confidence interval for
the slope of the population regression line that relates cancer mortality rate to index of exposure.
67)
A)
4.46 to 14.00
B)
4.26 to 14.20
C)
4.97 to 13.49
D)
5.11 to 13.35
Provide an appropriate response.
68)
Wassamatta University offers supplemental instruction (SI) for introductory chemistry students
three times a week. The table below shows the number of SI visits during the semester for a sample
of students along with each student’s final class average. Use technology to compute a p–value and
use it to determine whether the regression equation is useful for making predictions about the
benefit of attending SI. Test at the 5% significance level with the hypotheses H0: 1= 0 and Ha: 1
0.
# of SI visits Final class average
2
8
10
9
15
7
5
4
81
85
76
76
72
72
42
59
# of SI visits Final class average
8
10
7
7
5
4
4
11
81
71
66
88
63
62
61
70
68)
A)
p = 0.2633. Since p >, reject the null hypothesis H0: 1= 0. The regression equation is useful
for making predictions.
B)
p = 0.2529. Since p >, do not reject the null hypothesis H0: 1= 0. The regression equation is
not useful for making predictions.
C)
p = 0.04229. Since p <, reject the null hypothesis H0: 1= 0. The regression equation is
useful for making predictions.
D)
p = 0.0325. Since p <, do not reject the null hypothesis H0: 1= 0. The regression equation is
not useful for making predictions.
Obtain the required prediction interval. You may presume that the assumptions for regression inferences are met.
69)
^
Find a 95% prediction interval for the value of the response variable at x =5.
x 2 4 5 6
y 7 11 13 20 y= 3x
69)
A)
7.515 to 22.485
B)
3.969 to 26.031
C)
6.843 to 23.157
D)
1.969 to 24.031
Obtain the required confidence interval for the conditional mean. You may presume that the assumptions for regression
inferences are met.
70)
^
The sample data below are the index of exposure (x) to radioactive waste for nine different Oregon
counties and cancer mortality rate (y) (deaths per 100,000).
x 2.49 2.57 3.41 1.25 1.62 3.83 11.64 6.41 8.34
y 147.1 130.1 129.9 113.5 137.5 162.3 207.5 177.9 210.3 y= 114.72 + 9.23x
The standard error of the estimate is 14.0099. Determine a 95% confidence interval for the mean
cancer mortality rate of all counties whose index of exposure is 1.74.
70)
A)
119.0 to 142.6 deaths per 100,000
B)
116.1 to 145.5 deaths per 100,000
C)
94.5 to 167.1 deaths per 100,000
D)
116.7 to 144.8 deaths per 100,000
Provide an appropriate response.
71)
Suppose that variables x and y satisfy the assumptions for regression inferences. For samples of
size n, each with the same values for the predictor variable, what is the distribution of the slope b1,
of the sample regression line?
71)
A)
Normal with mean 1 and standard deviation se
B)
t–distribution with mean 1 and standard deviation / Sxx
C)
t–distribution with mean 1 and standard deviation se
D)
Normal with mean 1 and standard deviation / Sxx
Obtain the required point estimate of the mean or predicted y–value. You may presume that the assumptions for
regression inferences are met and that x is useful as a predictor of y.
72)
^
Applicants for a particular job, which involves extensive travel in Spanish speaking countries,
must take a proficiency test in Spanish. The sample data below were obtained in a study of the
relationship between the numbers of years applicants have studied Spanish (x) and their score on
the test (y).
x 3 4 4 2 5 3 4 5 3 2
y 57 78 72 58 89 63 73 84 75 48 y= 31.55 + 10.90x
Obtain an estimate of the mean score for all applicants who have studied Spanish for 2.1 years.
Round your answer to two decimal places.
72)
A)
42.45
B)
54.44
C)
33.65
D)
52.55
Obtain the required confidence interval for the slope of the population regression line. You may presume that the
assumptions for regression inferences are met.
73)
^
A set of sample data consisting of 22 pairs of x and y values yields a regression equation of
y= 5.93 + 0.19x. The standard error of the estimate is approximately 13.65 and Sxx =54,816.
Obtain a 95% confidence interval for the slope of the population regression line that relates y to x.
73)
A)
0.09 to 0.29
B)
0.04 to 0.34
C)
0.07 to 0.31
D)
5.81 to 6.05
74)
^
The sample data below are the typing speeds (in words per minute) and reading speeds (in words
per minute) of nine randomly selected secretaries. Here, x denotes typing speed, and y denotes
reading
speed.
x 60 56 52 63 70 58 44 79 62
y 370 551 528 348 645 454 503 618 500 y= 290.2 + 3.502x
The standard error of the estimate is approximately 100.33479. Find a 90% confidence interval for
the slope of the population regression line that relates reading speed to typing speed.
74)
A)
–1.48 to 8.48
B)
–3.17 to 10.17
C)
–3.05 to 10.05
D)
–1.42 to 8.42
75)
^
A grass seed company conducts a study to determine the relationship between the density of seeds
planted (in pounds per 500 sq ft) and the quality of the resulting lawn. Eight similar plots of land
are selected and each is planted with a particular density of seed. One month later the quality of
each lawn is rated on a scale of 0 to 100. The sample data are given below, where x denotes seed
density, and y denotes lawn quality.
x 1 1 2 3 3 3 4 5
y 30 40 40 40 50 65 50 50 y= 33.14 + 4.54x
The standard error of the estimate is approximately 9.0736. Find a 95% confidence interval for the
slope of the population regression line that relates lawn quality to seed density.
75)
A)
–1.50 to 10.58
B)
–1.30 to 10.38
C)
27.10 to 39.18
D)
–0.26 to 9.34
Provide an appropriate response.
76)
True or false? When performing regression analysis, different samples will all yield the same
sample regression line.
76)
A)
True
B)
False
77)
True or false? In the context of regression, the term “confidence” is usually reserved for interval
estimates of parameters while the term “prediction” is used for interval estimates of variables.
77)
A)
True
B)
False
Determine the standard error of the estimate.
78)
Two different tests are designed to measure employee dexterity and productivity. Several
employees are randomly selected and tested with the results below. Here, x denotes dexterity
score, and y denotes productivity score.
x
y 23 25 28 21 21 25 26 30 34 36
49 53 59 42 47 53 55 63 67 75
78)
A)
1.6511
B)
3.6700
C)
3.8926
D)
1.753
Provide an appropriate response.
79)
The table below gives the career free–throw percentage and the player height for a sample of NBA
basketball players, both past and present. Assuming that there is a relationship between height and
free–throw percentage, use Minitab to find a 95% confidence interval for the mean free–throw
percentage of all NBA players, past and present, with a playing height of 2.00 meters.
Height (meters) Career Free–throw %
1.83
2.16
2.13
2.26
2.11
2.01
1.83
1.98
76.0
54.2
71.0
81.1
75.6
78.2
90.4
82.1
Height (meters) Career Free–throw %
2.18
2.08
2.01
1.60
2.06
2.03
2.21
2.29
72.1
69.2
58.4
82.7
88.6
84.8
64.9
56.1
79)
A)
53.33% to 97.90%
B)
69.75% to 81.35%
C)
70.02% to 81.22%
D)
75.50% to 77.10%
Obtain the required confidence interval for the slope of the population regression line. You may presume that the
assumptions for regression inferences are met.
80)
^
Find a 90% confidence interval for the slope of the population regression line.
x 0 1 5 3 3
y 7 5 –4 0 1 y= 7.105 – 2.211x
80)
A)
–2.276 to –2.146
B)
(2.464 to –1.958
C)
2.440 to –1.982
D)
2.387 to –2.035
Provide an appropriate response.
81)
True or false? In the regression model, the predictor variable is useful in predicting the response
variable provided that 1= 0.
81)
A)
True
B)
False
Determine the standard error of the estimate.
82)
^
x 2 4 5 6
y 7 11 13 20 y= 3x
82)
A)
2.2361
B)
4.1892
C)
6.2750
D)
5.00
Obtain the required point estimate of the mean or predicted y–value. You may presume that the assumptions for
regression inferences are met and that x is useful as a predictor of y.
83)
^
A grass seed company conducts a study to determine the relationship between the density of seeds
planted (in pounds per 500 sq ft) and the quality of the resulting lawn. Eight similar plots of land
are selected and each is planted with a particular density of seed. One month later the quality of
each lawn is rated on a scale of 0 to 100. The sample data are given below, where x denotes seed
density, and y denotes lawn quality.
x 1 1 2 3 3 3 4 5
y 30 40 40 40 50 65 50 50 y= 33.14 + 4.54x
Use the data to obtain an estimate of the mean lawn quality for all lawns sown with a seed density
of 2.4. Round your answer to two decimal places.
83)
A)
44.04
B)
35.54
C)
40.08
D)
45.14
84)
^
The sample data below are the index of exposure (x) to radioactive waste for nine different Oregon
counties and cancer mortality rate (y) (deaths per 100,000).
x 2.49 2.57 3.41 1.25 1.62 3.83 11.64 6.41 8.34
y 147.1 130.1 129.9 113.5 137.5 162.3 207.5 177.9 210.3 y= 114.72 + 9.23x
Use the data to obtain an estimate of the mean cancer mortality rate for all counties whose index of
exposure is 8.68. Round your answer to one decimal place.
84)
A)
132.6 deaths per 100,000
B)
194.8 deaths per 100,000
C)
192.0 deaths per 100,000
D)
198.9 deaths per 100,000
85)
^
Determine a point estimate for the conditional mean at x =3.
x 3 2 4
y 8 4 6 y= 3 + x
85)
A)
6
B)
7
C)
3
D)
8
Determine the standard error of the estimate.
86)
The paired data below consists of heights and weights of 6 randomly selected adults. Here, x
denotes height, in meters, and y denotes weight, in kilograms.
x 1.61 1.72 1.78 1.80 1.67 1.88
y54 62 70 84 61 92
86)
A)
6.9205
B)
9.7944
C)
15.648
D)
5.0015
D)
Obtain the required prediction interval. You may presume that the assumptions for regression inferences are met.
87)
^
Ten students in a graduate program were randomly selected. Their grade point averages (GPAs)
when they entered the program were between 3.5 and 4.0. The following data consist of the
students’ GPAs (x) on entering the program and their current GPAs (y).
x 3.5 3.8 3.6 3.6 3.5 3.9 4.0 3.9 3.5 3.7
y 3.6 3.7 3.9 3.6 3.9 3.8 3.7 3.9 3.8 4.0 y= 3.67 + 0.0313x
The standard error of the estimate is approximately 0.14521. Determine a 99% prediction interval
for the current GPA of a student with an entering GPA of 3.8.
87)
A)
3.30 to 4.28
B)
3.34 to 4.24
C)
3.27 to 4.31
D)
3.61 to 3.97
D)
D)
Provide an appropriate response.
88)
The following table gives the US domestic oil production rates (excluding Alaska) over the past few
years. Assuming that the data can be modeled with a linear model, use technology to obtain the
standard error of the estimate.
Year Millions of barrels per day
1987 6.39
1988 6.12
1989 5.74
1990 5.58
1991 5.62
1992 5.46
1993 5.26
1994 5.10
Year Millions of barrels per day
1995 5.08
1996 5.07
1997 5.16
1998 5.08
1999 4.83
2000 4.85
2001 4.84
2002 4.83
88)
A)
0.18065
B)
–0.9287
C)
0.86257
D)
4.76095
Obtain the required prediction interval. You may presume that the assumptions for regression inferences are met.
89)
^
The sample data below are the typing speeds (in words per minute) and reading speeds (in words
per minute) of nine randomly selected secretaries. Here, x denotes typing speed, and y denotes
reading
speed.
x 60 56 52 63 70 58 44 79 62
y 370 551 528 348 645 454 503 618 500 y= 290.2 + 3.502x
The standard error of the estimate is se= 100.33479. Determine a 90% prediction interval for the
reading speed of a secretary whose typing speed is 49.
89)
A)
362.6 to 561.0 words per minute
B)
301.7 to 621.9 words per minute
C)
247.3 to 676.3 words per minute
D)
251.3 to 672.3 words per minute
Obtain the required point estimate of the mean or predicted y–value. You may presume that the assumptions for
regression inferences are met and that x is useful as a predictor of y.
90)
^
The sample data below are the typing speeds (in words per minute) and reading speeds (in words
per minute) of nine randomly selected secretaries. Here, x denotes typing speed, and y denotes
reading
speed.
x 60 56 52 63 70 58 44 79 62
y 370 551 528 348 645 454 503 618 500 y= 290.2 + 3.502x
Use the data to obtain an estimate of the mean reading speed for all secretaries whose typing speed
is 72. Round your answer to the nearest word.
90)
A)
521 words per minute
B)
362 words per minute
C)
557 words per minute
D)
542 words per minute
Obtain the required confidence interval for the slope of the population regression line. You may presume that the
assumptions for regression inferences are met.
91)
^
Ten students in a graduate program were randomly selected. Their grade point averages (GPAs)
when they entered the program were between 3.5 and 4.0. The following data consist of the
students’ GPAs (x) on entering the program and their current GPAs (y).
x 3.5 3.8 3.6 3.6 3.5 3.9 4.0 3.9 3.5 3.7
y 3.6 3.7 3.9 3.6 3.9 3.8 3.7 3.9 3.8 4.0 y= 3.67 + 0.0313x
The standard error of the estimate is approximately 0.14521. Obtain a 95% confidence interval for
the slope of the population regression line that relates current GPA to entering GPA.
91)
A)
–0.56 to 0.62
B)
–0.45 to 0.51
C)
–0.44 to 0.50
D)
–0.55 to 0.61
Provide an appropriate response.
92)
True or false? The sample linear correlation coefficient, r, measures the linear correlation of all
possible pairs of observations of the two variables.
92)
A)
True
B)
False
Determine the standard error of the estimate.
93)
^
x 9 7 2 3 4 22 17
y 43 35 16 21 23 102 81 y= 6.18286 + 4.33937x
93)
A)
2.6959
B)
3.1270
C)
0.8275
D)
1.6419
Provide an appropriate response.
94)
The maintenance costs incurred over the past year for a particular make, model, and year of
automobile are given below, along with each car’s end–of–year mileage. Use technology to
compute a p–value and use it to determine whether the regression equation is useful for making
predictions about maintenance costs for this automobile model. Test at the 1% significance level
with the hypotheses H0: 1= 0 and Ha: 1
0. Make sure to eliminate any outliers and/or
influential points from the data.
End–of–year mileage
(thousands of miles) Last year’s maintenance
cost (dollars)
23.1
58.2
44.6
50.2
27.5
38.9
38.1
36.8
119
198
161
270
122
151
148
133
94)
A)
p = 0.00014. Since p <, reject the null hypothesis. The regression equation is useful for
making maintenance cost predictions.
B)
p = 0.02317. Since p >, reject the null hypothesis. The regression equation is useful for
making maintenance cost predictions.
C)
p = 0.00014. Since p <, do not reject the null hypothesis. The regression equation is not
useful for making maintenance cost predictions.
D)
p = 0.02317. Since p >, do not reject the null hypothesis. The regression equation is not
useful for making maintenance cost predictions.
Determine the standard error of the estimate.
95)
^
x 3 2 4
y 8 4 6 y= 3 + x
95)
A)
1.1547
B)
2.00
C)
0.250
D)
2.4495
Obtain the required prediction interval. You may presume that the assumptions for regression inferences are met.
96)
^
Find a 95% prediction interval for the value of the response variable at x =3.
x 3 2 4
y 8 4 6 y= 3 + x
96)
A)
40.938 to 46.938
B)
–29.938 to 41.938
C)
–6.171 to 18.171
D)
–11.859 to 23.859
D)
Provide an appropriate response.
97)
True or false? In the regression model, if 1= 0, then for each value x of the predictor variable, the
conditional distribution of the response variable is a normal distribution with a mean which is
independent of x.
97)
A)
True
B)
False
Determine the standard error of the estimate.
98)
The paired data below consists of test scores and hours of preparation for 5 randomly selected
students. Here, x denotes hours of preparation, and y denotes test score.
x 5 2 9 6 10
y 64 48 72 73 80
98)
A)
4.1097
B)
7.1720
C)
13.060
D)
5.3999
D)
D)
Obtain the required confidence interval for the conditional mean. You may presume that the assumptions for regression
inferences are met.
99)
^
Ten students in a graduate program were randomly selected. Their grade point averages (GPAs)
when they entered the program were between 3.5 and 4.0. The following data consist of the
students’ GPAs (x) on entering the program and their current GPAs (y).
x 3.5 3.8 3.6 3.6 3.5 3.9 4.0 3.9 3.5 3.7
y 3.6 3.7 3.9 3.6 3.9 3.8 3.7 3.9 3.8 4.0 y= 3.67 + 0.0313x
The standard error of the estimate is approximately 0.14521. Determine a 99% confidence interval
for the mean current GPA of all students with an entering GPA of 3.9.
99)
A)
3.57 to 4.01
B)
3.59 to 3.99
C)
3.56 to 4.02
D)
3.25 to 4.33
Provide an appropriate response.
100)
True or false? In the context of regression analysis, the sum of the residuals is always zero.
100)
A)
True
B)
False
A
Obtain the required point estimate of the mean or predicted y–value. You may presume that the assumptions for
regression inferences are met and that x is useful as a predictor of y.
101)
^
Applicants for a particular job, which involves extensive travel in Spanish speaking countries,
must take a proficiency test in Spanish. The sample data below were obtained in a study of the
relationship between the numbers of years applicants have studied Spanish (x) and their score on
the test (y).
x 3 4 4 2 5 3 4 5 3 2
y 57 78 72 58 89 63 73 84 75 48 y= 31.55 + 10.90x
Use the data to predict the test score of an applicant who has studied Spanish for 3.4 years. Round
your answer to two decimal places.
101)
A)
34.95
B)
65.55
C)
42.45
D)
68.61
D
C
102)
^
Determine the predicted value of the response variable at x =3.
x 3 2 5 8
y 4 110 19 y= –5 + 3x
102)
A)
14
B)
–12
C)
4
D)
3
Obtain the required prediction interval. You may presume that the assumptions for regression inferences are met.
103)
^
Applicants for a particular job, which involves extensive travel in Spanish speaking countries,
must take a proficiency test in Spanish. The sample data below were obtained in a study of the
relationship between the numbers of years applicants have studied Spanish (x) and their score on
the test (y).
x 3 4 4 2 5 3 4 5 3 2
y 57 78 72 58 89 63 73 84 75 48 y= 31.55 + 10.90x
The standard error of the estimate is se= 5.651. Determine a 95% prediction interval for the score of
an applicant who has studied Spanish for 3.4 years.
103)
A)
55.2 to 82.0
B)
54.9 to 82.3
C)
57.6 to 79.6
D)
64.5 to 72.8
Determine the standard error of the estimate.
104)
^
x 0 1 5 3 3
y 7 5 –4 0 1 y= 7.105 – 2.211x
104)
A)
0.5130
B)
0.6483
C)
0.7280
D)
0.4189
Provide an appropriate response.
105)
The maintenance costs incurred over the past year for a particular make, model, and year of
automobile are given below, along with each car’s end–of–year mileage. Assuming that there is a
relationship between milage and maintenance cost, use Minitab to find a 95% confidence interval
for the mean maintenance cost for all cars with this particular make, and model, that have been
driven 40,000 miles.
End–of–year mileage
(thousands of miles) Last year’s maintenance
cost (dollars)
23.1
58.2
44.6
50.2
27.5
38.9
38.1
36.8
119
198
161
170
122
151
148
133
105)
A)
$135.49 to $166.47
B)
$138.68 to $163.29
C)
$145.82 to $156.15
D)
$146.88 to $155.09
Obtain the required confidence interval for the slope of the population regression line. You may presume that the
assumptions for regression inferences are met.
106)
^
Find a 90% confidence interval for the slope of the population regression line.
x 2 4 5 6
y 7 11 13 20 y= 3x
106)
A)
–0.612 to 2.612
B)
0.779 to 2.779
C)
0.793 to 5.207
D)
0.426 to 2.426
Obtain the required prediction interval. You may presume that the assumptions for regression inferences are met.
107)
^
A grass seed company conducts a study to determine the relationship between the density of seeds
planted (in pounds per 500 sq ft) and the quality of the resulting lawn. Eight similar plots of land
are selected and each is planted with a particular density of seed. One month later the quality of
each lawn is rated on a scale of 0 to 100. The sample data are given below, where x denotes seed
density, and y denotes lawn quality.
x 1 1 2 3 3 3 4 5
y 30 40 40 40 50 65 50 50 y= 33.14 + 4.54x
The standard error of the estimate is se= 9.0736. Determine a 99% prediction interval for the lawn
quality of a lawn sown with a seed density of 3.7.
107)
A)
12.2 to 84.0
B)
15.3 to 84.6
C)
18.8 to 81.1
D)
35.2 to 64.7
Provide an appropriate response.
108)
When performing a hypothesis test for the population linear correlation coefficient, , the test
statistic is t = r/ (1 –r2)/(n – 2). What is the distribution of this test statistic if the null hypothesis,
H0: = 0, is true?
108)
A)
normal distribution
B)
chi–square distribution with df = n – 2
C)
t–distribution with df = n – 2
D)
t–distribution with df = n – 1
C
Explanation:
Obtain the required confidence interval for the slope of the population regression line. You may presume that the
assumptions for regression inferences are met.
109)
^
Applicants for a particular job, which involves extensive travel in Spanish speaking countries,
must take a proficiency test in Spanish. The sample data below were obtained in a study of the
relationship between the numbers of years applicants have studied Spanish (x) and their score on
the test (y).
x 3 4 4 2 5 3 4 5 3 2
y 57 78 72 58 89 63 73 84 75 48 y= 31.55 + 10.90x
The standard error of the estimate is approximately 5.651. Find a 99% confidence interval for the
slope of the population regression line that relates test score to number of years of study.
109)
A)
9.09 to 12.7
B)
5.23 to 16.57
C)
5.05 to 16.75
D)
25.70 to 37.40
C
Explanation:
A
Explanation:
Provide an appropriate response.
110)
The maintenance costs incurred over the past year for a particular make, model, and year of
automobile are given below, along with each car’s end–of–year mileage. Assuming that there is a
relationship between milage and maintenance cost, use Minitab to find a 95% prediction interval
for the mean maintenance cost of Joe’s car (that is this particular make and model) that has 40,000
miles on it.
End–of–year mileage
(thousands of miles) Last year’s maintenance
cost (dollars)
23.1
58.2
44.6
50.2
27.5
38.9
38.1
36.8
119
198
161
170
122
151
148
133
110)
A)
$138.68 to $163.29
B)
$146.88 to $155.09
C)
$145.82 to $156.15
D)
$135.49 to $166.47
Obtain the required confidence interval for the conditional mean. You may presume that the assumptions for regression
inferences are met.
111)
^
A grass seed company conducts a study to determine the relationship between the density of seeds
planted (in pounds per 500 sq ft) and the quality of the resulting lawn. Eight similar plots of land
are selected and each is planted with a particular density of seed. One month later the quality of
each lawn is rated on a scale of 0 to 100. The sample data are given below, where x denotes seed
density, and y denotes lawn quality.
x 1 1 2 3 3 3 4 5
y 30 40 40 40 50 65 50 50 y= 33.14 + 4.54x
The standard error of the estimate is se= 9.0376. Determine a 99% confidence interval for the mean
lawn quality of all lawns sown with a seed density of 4.4.
111)
A)
28.7 to 75.1
B)
31.9 to 70.3
C)
30.8 to 71.8
D)
34.0 to 72.3
Obtain the required point estimate of the mean or predicted y–value. You may presume that the assumptions for
regression inferences are met and that x is useful as a predictor of y.
112)
^
The sample data below are the typing speeds (in words per minute) and reading speeds (in words
per minute) of nine randomly selected secretaries. Here, x denotes typing speed, and y denotes
reading
speed.
x 60 56 52 63 70 58 44 79 62
y 370 551 528 348 645 454 503 618 500 y= 290.2 + 3.502x
Use the data to predict the reading speed of a secretary whose typing speed is 64. Round your
answer to the nearest word.
112)
A)
496 words per minute
B)
514 words per minute
C)
527 words per minute
D)
354 words per minute
Determine the standard error of the estimate.
113)
^
x 3 2 5 8
y 4 110 19 y= –5 + 3x
113)
A)
0.17
B)
0
C)
1.29
D)
2.06
Obtain the required prediction interval. You may presume that the assumptions for regression inferences are met.
114)
^
The sample data below are the index of exposure (x) to radioactive waste for nine different Oregon
counties and cancer mortality rate (y) (deaths per 100,000).
x 2.49 2.57 3.41 1.25 1.62 3.83 11.64 6.41 8.34
y 147.1 130.1 129.9 113.5 137.5 162.3 207.5 177.9 210.3 y= 114.72 + 9.23x
The standard error of the estimate is 14.0099. Determine a 95% prediction interval for the cancer
mortality rate of a county whose index of exposure is 3.80.
114)
A)
114.7 to 184.9 deaths per 100,000
B)
138.4 to 161.2 deaths per 100,000
C)
121.7 to 177.9 deaths per 100,000
D)
116.2 to 183.4 deaths per 100,000
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