Deck 13: Inference in Linear Models
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Deck 13: Inference in Linear Models
1
In a study of reaction times, the time to respond to a visual stimulus (x) and the time to respond to an auditory stimulus (y) were recorded for each of 8 subjects. Times were measured in thousandths
Of a second. The results are presented in the following table.
Test H0:
=0 versus
. Use the
:=0.05 level of significance.
A) Do not reject H0
B) Reject H0
Of a second. The results are presented in the following table.

Test H0:



A) Do not reject H0
B) Reject H0
Reject H0
2
In a study of reaction times, the time to respond to a visual stimulus (x) and the time to respond to an auditory stimulus (y) were recorded for each of 8 subjects. Times were measured in thousandths
Of a second. The results are presented in the following table.
Construct a 95% confidence interval for the slope of the least-squares regression line.
A) (21.1376, 21.3239)
B) (0.7611, 0.9474)
C) (21.1134, 21.3481)
D) (0.7370, 0.9716)
Of a second. The results are presented in the following table.

A) (21.1376, 21.3239)
B) (0.7611, 0.9474)
C) (21.1134, 21.3481)
D) (0.7370, 0.9716)
(0.7370, 0.9716)
3

A) 1.3235
B) 9.9632
C) 68.0000
D) 1.9043
1.3235
4
The summary statistics for a certain set of points are: 
, and
Assume the conditions of the linear model hold. A 99% confidence interval for
will be constructed.
Test the null hypothesis
versus https://d2lvgg3v3hfg70.cloudfront.net/TB34225555/
. Use the
level of significance.
A) Reject H0
B) Do not reject H0

, and


Test the null hypothesis



A) Reject H0
B) Do not reject H0
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5

A) 0.005378
B) 3.388947
C) 12
D) 6.049805
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6
In a study of reaction times, the time to respond to a visual stimulus (x) and the time to respond to an auditory stimulus (y) were recorded for each of 8 subjects. Times were measured in thousandths
Of a second. The results are presented in the following table.
Compute the least-squares regression line for predicting auditory response time (y) from visual response Time (x).
A)
B)
C)
D)
Of a second. The results are presented in the following table.

A)

B)

C)

D)

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7
Use the given set of points to test the null hypothesis 
level of significance.

A) Reject H0
B) Do not reject H0

level of significance.

A) Reject H0
B) Do not reject H0
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8

A) 3.250
B) 2.821
C) 3.355
D) 2.896
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9
The summary statistics for a certain set of points are: n=10, se=3.199,
=11.257, and
=1.704 . Assume the conditions of the linear model hold. A 99% confidence interval for 11ec916b_6e28_0fa2_a226_b17a14146f0a_TB34225555_11 will be constructed.
i). How many degrees of freedom are there for the critical value?
ii). What is the critical value?
iii). What is the margin of error?
iv). Construct the 99% confidence interval.


i). How many degrees of freedom are there for the critical value?
ii). What is the critical value?
iii). What is the margin of error?
iv). Construct the 99% confidence interval.
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10

A) 1.7238
B) 10.1596
C) 1.4149
D) 23.5000
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11
Use the given set of points to compute the margin of error for a 95% confidence interval for
. 
A) 1.01
B) 0.4127
C) 2.6388
D) 2.0734


A) 1.01
B) 0.4127
C) 2.6388
D) 2.0734
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12

A) 2.1184
B) 0.1216
C) 1.2865
D) 111.8750
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13

A) 41.002571
B) 1.391921
C) 1.146365
D) 1.399143
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14
The following display from a TI-84 Plus calculator presents the results of a test of the null hypothesis
How many degrees of freedom did the calculator use?
A) 4
B) 7
C) 8
D) 6


A) 4
B) 7
C) 8
D) 6
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15
Use the given set of points to construct a 95% confidence interval for https://d2lvgg3v3hfg70.cloudfront.net/TB34225555/
.

A)
B)
C)
D)


A)

B)

C)

D)

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16
Use the given set of points to compute the residual standard deviation

A) 7.9164
B) 44.8750
C) 1.6379
D) 2.5696


A) 7.9164
B) 44.8750
C) 1.6379
D) 2.5696
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17
In a study of reaction times, the time to respond to a visual stimulus (x) and the time to respond to
an auditory stimulus (y) were recorded for each of 8 subjects. Times were measured in thousandths
of a second. The results are presented in the following table.
i). Compute the least-squares regression line for predicting auditory response time (y) from visual res time (x).
ii). Construct a 99% confidence interval for the slope of the least-squares regression line.
iii). Test H0:
=0 versus https://d2lvgg3v3hfg70.cloudfront.net/TB1209/
.Use the
=0.01 level of significance.
an auditory stimulus (y) were recorded for each of 8 subjects. Times were measured in thousandths
of a second. The results are presented in the following table.

ii). Construct a 99% confidence interval for the slope of the least-squares regression line.
iii). Test H0:



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18
Use the given set of points to
a). Compute b1.
b). Compute the residual standard deviation se.
c). Compute the sum of squares for x,
d). Compute the standard error of b1, sb.
e). Find the critical value for a 95% confidence interval for
f). Compute the margin of error for a 95% confidence interval for
g). Construct a 95% confidence interval for
h). Test the null hypothesis
versus
Use the
=0.05 level of significance.

a). Compute b1.
b). Compute the residual standard deviation se.
c). Compute the sum of squares for x,

d). Compute the standard error of b1, sb.
e). Find the critical value for a 95% confidence interval for

f). Compute the margin of error for a 95% confidence interval for

g). Construct a 95% confidence interval for

h). Test the null hypothesis




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19
The summary statistics for a certain set of points are:
, and
Assume the conditions of the linear model hold. A 95% confidence interval for
will be constructed.
Construct the 95% confidence interval.
A)
B)
C)
D)



Construct the 95% confidence interval.
A)

B)

C)

D)

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20

A) 22
B) 23
C) 21
D) 24
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21

A) (57.40, 63.18)
B) (56.52, 64.05)
C) (58.77, 61.81)
D) (58.31, 62.26)
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22
Use the given set of points to
a). Compute
and https://d2lvgg3v3hfg70.cloudfront.net/TB34225555/
.
b). Compute the predicted value
for the given value of x.
c). Compute the residual standard deviation
d). Compute the sum of squares for
e). Find the critical value for a 95% confidence or prediction interval.
f). Construct a 95% confidence interval for the mean response for the given value of x.
g). Construct a 95% prediction interval for an individual response for the given value of x.

a). Compute


b). Compute the predicted value

c). Compute the residual standard deviation

d). Compute the sum of squares for

e). Find the critical value for a 95% confidence or prediction interval.
f). Construct a 95% confidence interval for the mean response for the given value of x.
g). Construct a 95% prediction interval for an individual response for the given value of x.

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23

A) 15.666667
B) 65.333333
C) 2.475389
D) 4.112245
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24

A) 3.191939
B) 0.730472
C) 16.166667
D) 4.230326
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25
In a study of reaction times, the time to respond to a visual stimulus (x) and the time to respond to
an auditory stimulus (y) were recorded for each of 8 subjects. Times were measured in thousandths of
a second. The results are presented in the following table.
i). Compute a point estimate for the mean auditory response time for subjects with a visual response time of
183.
ii). Construct a 99% confidence interval for the mean auditory response time for subjects with a
visual response time of 183.
iii). Predict the auditory response time for a particular subject whose visual response time of 183.
iv). Construct a 99% prediction interval for the auditory response time for a particular subject whose
visual response time is 183.
an auditory stimulus (y) were recorded for each of 8 subjects. Times were measured in thousandths of
a second. The results are presented in the following table.

183.
ii). Construct a 99% confidence interval for the mean auditory response time for subjects with a
visual response time of 183.
iii). Predict the auditory response time for a particular subject whose visual response time of 183.
iv). Construct a 99% prediction interval for the auditory response time for a particular subject whose
visual response time is 183.
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26
The following display from a TI-84 Plus calculator presents the results of a test of the null hypothesis 

Can you conclude that the explanatory variable is useful in predicting the outcome variable? Answer this question using the
level of significance.
A) No
B) Yes


Can you conclude that the explanatory variable is useful in predicting the outcome variable? Answer this question using the

A) No
B) Yes
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27
In a study of reaction times, the time to respond to a visual stimulus (x) and the time to respond to an auditory stimulus (y) were recorded for each of 8 subjects. Times were measured in thousandths of
A second. The results are presented in the following table.
Compute a point estimate for the mean auditory response time for subjects with a visual response time of .
A) 249.98
B) 247.11
C) 244.25
D) 244.24
A second. The results are presented in the following table.

A) 249.98
B) 247.11
C) 244.25
D) 244.24
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28

A) 2.454834
B) 6.956787
C) 8
D) 0.039637
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29
In a study of reaction times, the time to respond to a visual stimulus (x) and the time to respond to an auditory stimulus (y) were recorded for each of 8 subjects. Times were measured in thousandths of
A second. The results are presented in the following table.
Construct a 99% confidence interval for the mean auditory response time for subjects with a visual
Response time of 171.
A) (231.15, 248.69)
B) (235.56, 244.28)
C) (236.23, 243.61)
D) (229.58, 250.26)
A second. The results are presented in the following table.

Response time of 171.
A) (231.15, 248.69)
B) (235.56, 244.28)
C) (236.23, 243.61)
D) (229.58, 250.26)
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30
In a study of reaction times, the time to respond to a visual stimulus (x) and the time to respond to an auditory stimulus (y) were recorded for each of 6 subjects. Times were measured in thousandths of
A second. The results are presented in the following table.
The following MINITAB output describes the fit of a linear model to these data. Assume that the assumptions
Of the linear model are satisfied.
Can you conclude that the response time to visual stimulus is useful in predicting the response time for
Auditory stimulus? Answer this question using the α = 0.05 level of significance.
A) Yes
B) No
A second. The results are presented in the following table.
The following MINITAB output describes the fit of a linear model to these data. Assume that the assumptions
Of the linear model are satisfied.

Auditory stimulus? Answer this question using the α = 0.05 level of significance.
A) Yes
B) No
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31
The following MINITAB output presents a 95% confidence interval for the mean ozone level on days when the relative humidity is 55%, and a 95% prediction interval for the ozone level on a
Particular day when the relative humidity is 55%. The units of ozone are parts per billion.
A) 55.0
B) 1.4
C) 38.46
D) 35.72
Particular day when the relative humidity is 55%. The units of ozone are parts per billion.

A) 55.0
B) 1.4
C) 38.46
D) 35.72
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32
Use the given set of points to compute b0 and b1.

A) b0=0 ; b1=3.860274
B) b0=10.572603 ; b1=3.860274
C) b0=3.860274 ; b1=10.572603
D) b0=14.833333 ; b1=10.572603

A) b0=0 ; b1=3.860274
B) b0=10.572603 ; b1=3.860274
C) b0=3.860274 ; b1=10.572603
D) b0=14.833333 ; b1=10.572603
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33
In a study of reaction times, the time to respond to a visual stimulus (x) and the time to respond to an auditory stimulus (y) were recorded for each of 8 subjects. Times were measured in thousandths of
A second. The results are presented in the following table.
Construct a 95% prediction interval for the auditory response time for a particular subject whose
Visual response time is 182.
A) (235.94, 250.26)
B) (240.33, 245.87)
C) (240.9, 245.3)
D) (237.42, 248.78)
A second. The results are presented in the following table.

Visual response time is 182.
A) (235.94, 250.26)
B) (240.33, 245.87)
C) (240.9, 245.3)
D) (237.42, 248.78)
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34
In a study of reaction times, the time to respond to a visual stimulus (x) and the time to respond to an auditory stimulus (y) were recorded for each of 8 subjects. Times were measured in thousandths of
A second. The results are presented in the following table.
Predict the auditory response time for a particular subject whose visual response time of 178.
A) 238.66
B) 242.11
C) 246.88
D) 245.56
A second. The results are presented in the following table.

A) 238.66
B) 242.11
C) 246.88
D) 245.56
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35
In a study of reaction times, the time to respond to a visual stimulus (x) and the time to respond to an auditory stimulus (y) were recorded for each of 6 subjects. Times were measured in thousandths of
A second. The results are presented in the following table.
What is the intercept of the least-squares regression line?
A) 0.286943
B) 19.54587
C) 0.051998
D) 204.285245
A second. The results are presented in the following table.

A) 0.286943
B) 19.54587
C) 0.051998
D) 204.285245
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36
In a study of reaction times, the time to respond to a visual stimulus (x) and the time to respond to an auditory stimulus (y) were recorded for each of 6 subjects. Times were measured in thousandths of
A second. The results are presented in the following table.
The following MINITAB output describes the fit of a linear model to these data. Assume that the assumptions
Of the linear model are satisfied.

What is the slope of the least-squares regression line?
A) 0.4671
B) 0.081367
C) 9.916568
D) 169.803813
A second. The results are presented in the following table.
The following MINITAB output describes the fit of a linear model to these data. Assume that the assumptions
Of the linear model are satisfied.

What is the slope of the least-squares regression line?
A) 0.4671
B) 0.081367
C) 9.916568
D) 169.803813
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37

A) (90.66, 91.49)
B) (90.54, 91.62)
C) (90.10, 92.05)
D) (89.81, 92.34)
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38

A) (0.59, 6.57)
B) (1.24, 5.92)
C) (0.72, 6.44)
D) (0, 5.92)
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39
Use the given set of points to compute the predicted value
for the given value of x.

A) 47.2615
B) 57.8
C) 130.4
D) 126.4615


A) 47.2615
B) 57.8
C) 130.4
D) 126.4615
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40
The following MINITAB output presents a 95% confidence interval for the mean ozone level on days when the relative humidity is 40%, and a 95% prediction interval for the ozone level on a
Particular day when the relative humidity is 40%. The units of ozone are parts per billion.
A) (41.23, 47.11)
B) (28.00, 60.34)
C) (40, 95)
D) (1.5, 44.17)
Particular day when the relative humidity is 40%. The units of ozone are parts per billion.

A) (41.23, 47.11)
B) (28.00, 60.34)
C) (40, 95)
D) (1.5, 44.17)
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41
The following MINITAB output presents a confidence interval for a mean response and a prediction
interval for an individual response.
What is the 95% confidence interval for the mean response?
interval for an individual response.

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42
The following MINITAB output presents a multiple regression equatior
=b0+b1x1+b2x2+b3x3+b4x4

It is desired to drop one of the explanatory variables. Which of the following is the most appropriate action?
A) Drop x4, then see whether R2 increases
B) Drop x1, then see whether R2 increases
C) Drop x4, then see whether adjusted R2 increases
D) Drop x1, then see whether adjusted R2 increases


It is desired to drop one of the explanatory variables. Which of the following is the most appropriate action?
A) Drop x4, then see whether R2 increases
B) Drop x1, then see whether R2 increases
C) Drop x4, then see whether adjusted R2 increases
D) Drop x1, then see whether adjusted R2 increases
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43
Construct the multiple regression sequence
=b0+b1x1+b2x2+b3x3 for the following data set:

A) 11ecb400_8919_50a3_8ce8_fd19d1580fc5_TB1209_11=3.8708+0.2200 x1-0.1503 x2+22.4605 x3
B) 11ecb400_8919_50a3_8ce8_fd19d1580fc5_TB1209_11=3.5766+0.1982 x1-0.1453 x2+22.0113 x3
C) 11ecb400_8919_50a3_8ce8_fd19d1580fc5_TB1209_11=22.0113-0.1453 x1+0.1982 x2+3.5766 x3
D) 11ecb400_8919_50a3_8ce8_fd19d1580fc5_TB1209_11=22.4605-0.1503 x1+0.2200 x2+3.8708 x3


A) 11ecb400_8919_50a3_8ce8_fd19d1580fc5_TB1209_11=3.8708+0.2200 x1-0.1503 x2+22.4605 x3
B) 11ecb400_8919_50a3_8ce8_fd19d1580fc5_TB1209_11=3.5766+0.1982 x1-0.1453 x2+22.0113 x3
C) 11ecb400_8919_50a3_8ce8_fd19d1580fc5_TB1209_11=22.0113-0.1453 x1+0.1982 x2+3.5766 x3
D) 11ecb400_8919_50a3_8ce8_fd19d1580fc5_TB1209_11=22.4605-0.1503 x1+0.2200 x2+3.8708 x3
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44
The following table lists values measured for 10 consecutive eruptions of the geyser Old Faithful in Yellowstone National Park. They are the duration, in minutes, of the eruption
, the dormant
Period before the eruption
, and the dormant period after the eruption (y).
Construct the multiple regression equation
=b0+b1x1+b2x2
A) 11ecb400_b9ed_77b4_8ce8_434575de6d27_TB1209_11=122.22-1.85 x1-0.62 x2
B) 11ecb400_b9ed_77b4_8ce8_434575de6d27_TB1209_11=118.78-1.7675 x1-0.5856 x2
C) 11ecb400_b9ed_77b4_8ce8_434575de6d27_TB1209_11=-0.62-1.85 x1+122.22 x2
D) 11ecb400_b9ed_77b4_8ce8_434575de6d27_TB1209_11=-0.5856-1.7675 x1+118.78 x2

Period before the eruption


Construct the multiple regression equation

A) 11ecb400_b9ed_77b4_8ce8_434575de6d27_TB1209_11=122.22-1.85 x1-0.62 x2
B) 11ecb400_b9ed_77b4_8ce8_434575de6d27_TB1209_11=118.78-1.7675 x1-0.5856 x2
C) 11ecb400_b9ed_77b4_8ce8_434575de6d27_TB1209_11=-0.62-1.85 x1+122.22 x2
D) 11ecb400_b9ed_77b4_8ce8_434575de6d27_TB1209_11=-0.5856-1.7675 x1+118.78 x2
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45

A) 50.0%
B) 42.3%
C) 0.3%
D) 7.7396%
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46

A) Yes
B) No
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47
The following MINITAB output presents a multiple regression equatior
=b0+b1x1+b2x2+b3x3+b4x4

Let
be the coefficient
Test the hypothesis
versus
level. What do you conclude?
A) Reject H0
B) Do not reject H0


Let




A) Reject H0
B) Do not reject H0
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48

A) 9.798
B) 9.8031
C) 10.6228
D) 11.7599
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49
The following MINITAB output presents a confidence interval for a mean response and a prediction
interval for an individual response.
interval for an individual response.

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50
The following MINITAB output presents a 95% confidence interval for the mean ozone level on days when the relative humidity is 40%, and a 95% prediction interval for the ozone level on a
Particular day when the relative humidity is 40%. The units of ozone are parts per billion.
Predict the ozone level for a day when the relative humidity is 40%.
A) 35.82
B) 40.0
C) 1.3
D) 38.37
Particular day when the relative humidity is 40%. The units of ozone are parts per billion.

A) 35.82
B) 40.0
C) 1.3
D) 38.37
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51
The following MINITAB output presents a multiple regression equatior
=b0+b1x1+b2x2+b3x3+b4x4

Let
be the coefficient
Test the hypothesis
rersus 
level. What do you conclude?
A) Do not H0
B) Reject H0


Let




level. What do you conclude?
A) Do not H0
B) Reject H0
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