Question 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.

$\begin{array} { c c } 
\hline \text { Visual } & \text { Auditory } \
\hline 185 & 244 \
204 & 244 \
242 & 247 \
209 & 245 \
191 & 243 \
250 & 249 \
155 & 237 \
188 & 245 \
\hline
\end{array}$

Compute a point estimate for the mean auditory response time for subjects with a visual response time of .

Accepted Answer

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

Question 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.

$\begin{array} { c c } 
\hline \text { Visual } & \text { Auditory } \
\hline 166 & 241 \
192 & 242 \
242 & 250 \
188 & 244 \
232 & 252 \
240 & 254 \
197 & 245 \
203 & 247 \
\hline
\end{array}$

Predict the auditory response time for a particular subject whose visual response time of 178.

Accepted Answer

A)   238.66
B)   242.11
C)   246.88
D)   245.56  B

Question 3

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.

$\begin{array} { c c } 
\hline \text { Visual } & \text { Auditory } \
\hline 168 & 243 \
233 & 253 \
169 & 242 \
204 & 243 \
206 & 248 \
202 & 245 \
157 & 239 \
240 & 248 \
\hline
\end{array}$

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.

Accepted Answer

i). 243.34
ii). (239.85, 246.83)
iii). 243.34
iv). (233.86, 252.82)

Question 4

The following display from a TI-84 Plus calculator presents the results of a test of the null hypothesis $H _ { 0 } : \beta _ { 1 } = 0$.

What is the value of the test statistic?

Accepted Answer

A)   0.005378
B)   3.388947
C)   12
D)   6.049805

Question 5

The summary statistics for a certain set of points are: $n = 12 , s _ { \mathrm { e } } = 3.505 , \quad \sum ( x - \bar { x } ) ^ { 2 } = 14.353$ , and $b _ { 1 } = 1.560$ Assume the conditions of the linear model hold. A 95% confidence interval for $\beta _ { 1 }$ will be constructed.
Construct the 95% confidence interval.

Accepted Answer

A)    −0.1164<β1<3.2364- 0.1164 < \beta _ { 1 } < 3.2364−0.1164<β1​<3.2364 
B)    −0.4763<β1<3.5963- 0.4763 < \beta _ { 1 } < 3.5963−0.4763<β1​<3.5963 
C)    −0.1016<β1<3.5963- 0.1016 < \beta _ { 1 } < 3.5963−0.1016<β1​<3.5963 
D)    −0.5013<β1<3.6213- 0.5013 < \beta _ { 1 } < 3.6213−0.5013<β1​<3.6213

Question 6

The following MINITAB output presents a multiple regression equatior $\hat { y }$=b0+b1x1+b2x2+b3x3+b4x4
The regression equation is
$$\mathrm { Y } = 4.7712 + 0.2662 \mathrm { X } 1 + 1.2710 \mathrm { X } 2 - 1.1349 \mathrm { X } 3 - 1.8545 \mathrm { X } 4$$
$\begin{array}{lllll}
\text { Predictor } & \text { Coef } & \text { SE Coef } & \text { T } & \mathrm{P} \
\text { Constant } & 4.7712 & 0.7648 & 0.92800 & 0.3280 \
\mathrm{X} 1 & 0.2662 & 0.8036 & -0.93740 & 0.3570 \
\mathrm{X} 2 & 1.2710 & 0.8451 & 1.74170 & 0.0830 \
\mathrm{X} 3 & -1.1349 & 0.6318 & -2.94990 & 0.0080 \
\mathrm{X} 4 & -1.8545 & 0.6753 & 3.27200 & 0.0020
\end{array}$

$\text { Analysis of Variance }$
$\begin{array}{lccccc}
\text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F } & \text { P } \
\text { Regression } & 4 & 624.2 & 156.1 & 9.8797 & 0.003 \
\text { Residual Error } & 40 & 633.7 & 15.8 & & \
\text { Total } & 44 & 1,257.9 & & & \
\hline
\end{array}$

It is desired to drop one of the explanatory variables. Which of the following is the most appropriate action?

Accepted Answer

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

Question 7

The summary statistics for a certain set of points are: $n = 17 , s _ { \mathrm { e } } = 2.880 , \sum ( x - \bar { x } ) ^ { 2 } = 19.241$, and $b _ { 1 } = 1.839$. Assume the conditions of the linear model hold. A $95 \%$ confidence interval for $\beta _ { 1 }$ will be constructed. What is the margin of error?

Accepted Answer

A)   41.002571
B)   1.391921
C)   1.146365
D)   1.399143

Question 8

Use the given set of points to construct a $95 \%$ confidence interval for the mean response for the given value of $x$.

Accepted Answer

A)   (57.40, 63.18) 
B)   (56.52, 64.05) 
C)   (58.77, 61.81) 
D)   (58.31, 62.26)

Question 9

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.

$\begin{array} { c c } 
\hline \text { Visual } & \text { Auditory } \
\hline 208 & 249 \
200 & 244 \
245 & 254 \
234 & 249 \
155 & 243 \
211 & 248 \
189 & 244 \
206 & 247 \
\hline
\end{array}$

Test H0:$\beta _ { 1 }$=0 versus $\beta _ { 1 } \neq 0$ . Use the $\alpha$ :=0.05 level of significance.

Accepted Answer

A)   Do not reject H0
B)   Reject H0

Question 10

The following display from a TI-84 Plus calculator presents the results of a test of the null hypothesis $H _ { 0 } : \beta _ { 1 } = 0$

Can you conclude that the explanatory variable is useful in predicting the outcome variable? Answer this question using the $\alpha = 0.05$ level of significance.

Accepted Answer

A) True 
 B)False

Question 11

The following display from a TI-84 Plus calculator presents the results of a test of the null hypothesis $H _ { 0 } : \beta _ { 1 } = 0$.

What is the P-value?

Accepted Answer

A)   2.454834
B)   6.956787
C)   8
D)   0.039637

Question 12

For a sample of size 15 , the following values were obtained: $b _ { 0 } = 3.58 , b _ { 1 } = 4.79 , s _ { \mathrm { e } } = 4.09$, $\sum ( x - \bar { x } ) ^ { 2 } = 237.89$, and $\bar { x } = 3.00$
Construct a $95 \%$ confidence interval for the mean response when $x = 0$.

Accepted Answer

A)   (0.59, 6.57) 
B)   (1.24, 5.92) 
C)   (0.72, 6.44) 
D)   (0, 5.92)

Question 13

The summary statistics for a certain set of points are: $n = 23 , s _ { \mathrm { e } } = 2.302 , \sum ( x - \bar { x } ) ^ { 2 } = 15.372$, and $b _ { 1 } = 1.902$. Assume the conditions of the linear model hold. A $99 \%$ confidence interval for $\beta _ { 1 }$ will be constructed. How many degrees of freedom are there for the critical value?

Accepted Answer

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

Question 14

Use the given set of points to
a). Compute $b _ { 0 }$ and $b _ { 1 }$.
b). Compute the predicted value $\hat { y }$ for the given value of x.
c). Compute the residual standard deviation $s _ { \mathrm { e } }$
d). Compute the sum of squares for $x , \quad \sum ( x - \bar { x } ) ^ { 2 }$
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.
$\begin{array} { l | l l l l l l } 
x & 12 & 10 & 19 & 15 & 11 & 15 \
\hline y & 31 & 28 & 46 & 39 & 31 & 37
\end{array} \quad x = 16$

Accepted Answer

The answer of Use the given set of points to
a)....

Question 15

The summary statistics for a certain set of points are: n=10, s_e=3.199, $\sum { ( x - \bar { x } ) ^ { 2 } }$ =11.257, and $\beta _ { 1 }$=1.704 . Assume the conditions of the linear model hold. A 99% confidence interval for $\beta _ { 1 }$ 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.

Accepted Answer

The answer of The summary statistics for a certain set...

Question 16

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. 
The regression equation is Auditory $= 169.803813 + 0.4671$ Visual

$\begin{array} { l l l l l } \text { Predictor } & \text { Coef } & \text { SE Coef } & \text { T } & \text { P } \ \text { Constant } & 169.803813 & 17.123244 & 9.916568 & 0.000581 \ \text { Visual } & 0.4671 & 0.081367 & 5.740635 & 0.004563 \end{array}$
What is the slope of the least-squares regression line?

Accepted Answer

A)   0.4671
B)   0.081367
C)   9.916568
D)   169.803813

Question 17

The following MINITAB output presents a confidence interval for a mean response and a prediction interval for an individual response. 
What is the $95 \%$ prediction interval for the new observation?

Accepted Answer

The answer of The following MINITAB output presents a confidence...

Question 18

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. Predicted Values for New Observations

$\begin{array} { l r c c c } \text { New Obs } & \text { Fit } & \text { SE Fit } & 95.0 \% \text { CI } & 95.0 \% \text { PI } \ 1 & 38.37 & 1.3 & ( 35.82,40.92 ) & ( 21.16,55.58 ) \end{array}$

Values of Predictors for New Observations

Predict the ozone level for a day when the relative humidity is 40%.

Accepted Answer

A)   35.82
B)   40.0
C)   1.3
D)   38.37

Question 19

The following MINITAB output presents a multiple regression equatior $\hat { y }$=b0+b1x1+b2x2+b3x3+b4x4
The regression equation is
$$\mathrm { Y } = 5.5079 + 1.6552 \mathrm { X } 1 - 1.1088 \mathrm { X } 2 + 1.3981 \mathrm { X } 3 - 1.2465 \mathrm { X } 4$$

$\begin{array}{lllll}
\text { Predictor } & \text { Coef } & \text { SE Coef } & \text { T } & \text { P } \
\text { Constant } & 5.5079 & 0.7640 & 1.1002 & 0.314 \
\text { X1 } & 1.6552 & 0.7032 & 3.1929 & 0.002 \
\text { X2 } & -1.1088 & 0.6023 & -3.2310 & 0.005 \
\text { X3 } & 1.3981 & 0.8970 & 1.8137 & 0.087 \
\text { X4 } & -1.2465 & 0.8251 & -1.1433 & 0.354
\end{array}$

$\text { Analysis of Variance }$
$\begin{array}{lccccc}
\text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F } & \text { P } \
\text { Regression } & 4 & 637.5 & 159.4 & 7.1480 & 0.003 \
\text { Residual Error } & 40 & 893.2 & 22.3 & & \
\text { Total } & 44 & 1,530.7 & & &
\end{array}$

Let $\beta _ { 1 }$ be the coefficient $X _ { 1 }$ Test the hypothesis $H _ { 0 } : \beta _ { 1 } = 0$ rersus $H _ { 1 } : \beta _ { 1 } \neq 0 \text { at the } \alpha = 0.05$
level. What do you conclude?

Accepted Answer

A)   Do not H0
B)   Reject H0

Question 20

Use the given set of points to a). Compute b₁. b). Compute the residual standard deviation s_e. c). Compute the sum of squares for x, $\sum ( x - \bar { x } ) ^ { 2 }$ d). Compute the standard error of b₁, s_b. e). Find the critical value for a 95% confidence interval for $\beta_1$ f). Compute the margin of error for a 95% confidence interval for $\beta_1$ g). Construct a 95% confidence interval for $\beta _ { 1 }$ h). Test the null hypothesis $H _ { 0 } : \beta _ { 1 } = 0$ versus $H _ { 1 } : \beta _ { 1 } \neq 0$ Use the$a$=0.05 level of significance. $\begin{array} { c | c c c c c c c c } x & 8 & 11 & 15 & 13 & 6 & 8 & 12 & 13 \ \hline y & 23 & 27 & 37 & 33 & 17 & 20 & 29 & 36 \end{array}$

Accepted Answer

The answer of Use the given set of points to
a)....

Exam 13: Inference in Linear Models

For a sample of size 15 , the following values were obtained: $b _ { 0 } = 3.58 , b _ { 1 } = 4.79 , s _ { \mathrm { e } } = 4.09$ , $\sum ( x - \bar { x } ) ^ { 2 } = 237.89$ , and $\bar { x } = 3.00$ Construct a $95 \%$ confidence interval for the mean response when $x = 0$ .

Exam 13: Inference in Linear Models

The following display from a TI-84 Plus calculator presents the results of a test of the null hypothesis H0:β1=0H _ { 0 } : \beta _ { 1 } = 0H0​:β1​=0 . What is the value of the test statistic?

Use the given set of points to construct a 95%95 \%95% confidence interval for the mean response for the given value of xxx .

The following display from a TI-84 Plus calculator presents the results of a test of the null hypothesis H0:β1=0H _ { 0 } : \beta _ { 1 } = 0H0​:β1​=0 . What is the P-value?

The following MINITAB output presents a confidence interval for a mean response and a prediction interval for an individual response. What is the 95%95 \%95% prediction interval for the new observation?