Consider the following pairs of observations. Complete parts a through f below. 1 4 2 4 a. Construct a scatterplot of the data. OA. OA. 0- Ay 8- 8- y X Ay 8 Q b. Use the method of least squares to fit a straight line to the six data points. y=+x (Round to three decimal places as needed.) c. Plot the least squares line on the scatterplot of part a. OB. Q Ay 8- OB. Ay 8+ 0- Q 0 5 5 O C. 84 0- 0 O C. 8- 3 3 Q a OD. Ay 8- OD. Aу 8- 0- 4 4 Q G to test whether the data provide sufficient evidence to indicate that x contributes information for the (U

College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter3: Polynomial Functions
Section3.5: Mathematical Modeling And Variation
Problem 2ECP
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Consider the following pairs of observations. Complete parts a through f below.
4
2
a. Construct a scatterplot of the data.
O A.
8
0-
0-
O A.
8-
Ay
0
Ay
y
X
X
8
8
Q
Q
b. Use the method of least squares to fit a straight line to the six data points.
y=+x (Round to three decimal places as needed.)
c. Plot the least squares line on the scatterplot of part a.
O B.
Q
Ay
8-
0-
О в.
Ay
8+
0-
4
Q
Q
Q
5
5
O C.
Ay
8-
0-
0
O C.
8+
0
3
3
8
X
8
Q
Q
G
Q
Q
O D.
Ay
8-
0-
0
O D.
Ay
8+
0-
0
4
4
X
8
Q
. Specify the null and alternative hypotheses that should be used to test whether the data provide sufficient evidence to indicate that x contributes information for the (lim
Transcribed Image Text:Consider the following pairs of observations. Complete parts a through f below. 4 2 a. Construct a scatterplot of the data. O A. 8 0- 0- O A. 8- Ay 0 Ay y X X 8 8 Q Q b. Use the method of least squares to fit a straight line to the six data points. y=+x (Round to three decimal places as needed.) c. Plot the least squares line on the scatterplot of part a. O B. Q Ay 8- 0- О в. Ay 8+ 0- 4 Q Q Q 5 5 O C. Ay 8- 0- 0 O C. 8+ 0 3 3 8 X 8 Q Q G Q Q O D. Ay 8- 0- 0 O D. Ay 8+ 0- 0 4 4 X 8 Q . Specify the null and alternative hypotheses that should be used to test whether the data provide sufficient evidence to indicate that x contributes information for the (lim
d. Specify the null and alternative hypotheses that should be used to test whether the data provide sufficient evidence to indicate that x contributes information for the (linear) prediction
O A. Ho: B₁ = 0, H₂: B₁ #0
OB. Ho: B₁=0, Ha: B₁ >0
OC. Ho: Po=0, Ha: Bo >0
OD. Ho: Bo=0, Ha: Bo #0
O E. Ho: Bo=0, Ha: Bo <0
OF. Ho: B₁ = 0, H₂: B₁ <0
e. What is the test statistic that should be used in conducting the hypothesis test of part d? Specify the degrees of freedom associated with the test statistic.
The test statistic is t = (Round to two decimal places as needed.)
The associated degrees of freedom is df =
f. Conduct the hypothesis test of part d, using a = 0.05.
Find the p-value.
p-value= (Round to three decimal places as needed.)
Make the appropriate conclusion.
O A. Do not reject Ho. There is insufficient evidence that x contributes information for the prediction of y.
OB. Reject Ho. There is sufficient evidence that x contributes information for the prediction of y.
OC. Do not reject Ho. There is sufficient evidence that x contributes information for the prediction of y.
O D. Reject Ho. There is insufficient evidence that x contributes information for the prediction of y.
Transcribed Image Text:d. Specify the null and alternative hypotheses that should be used to test whether the data provide sufficient evidence to indicate that x contributes information for the (linear) prediction O A. Ho: B₁ = 0, H₂: B₁ #0 OB. Ho: B₁=0, Ha: B₁ >0 OC. Ho: Po=0, Ha: Bo >0 OD. Ho: Bo=0, Ha: Bo #0 O E. Ho: Bo=0, Ha: Bo <0 OF. Ho: B₁ = 0, H₂: B₁ <0 e. What is the test statistic that should be used in conducting the hypothesis test of part d? Specify the degrees of freedom associated with the test statistic. The test statistic is t = (Round to two decimal places as needed.) The associated degrees of freedom is df = f. Conduct the hypothesis test of part d, using a = 0.05. Find the p-value. p-value= (Round to three decimal places as needed.) Make the appropriate conclusion. O A. Do not reject Ho. There is insufficient evidence that x contributes information for the prediction of y. OB. Reject Ho. There is sufficient evidence that x contributes information for the prediction of y. OC. Do not reject Ho. There is sufficient evidence that x contributes information for the prediction of y. O D. Reject Ho. There is insufficient evidence that x contributes information for the prediction of y.
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