A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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![Values of modulus of elasticity (MOE, the ratio of stress, i.e., force per unit area, to strain, i.e., deformation per unit length, in GPa) and flexural strength (a measure of the ability to resist failure in bending, in MPa) were
determined for a sample of concrete beams of a certain type, resulting in the following data:
МОЕ
29.9
33.3
33.6
35.4
35.6
36.0
36.3
36.4
37.6
37.6
Strength
6.0
7.1
7.4
6.2
8.2
6.9
6.9
7.7
6.7
6.6
МОЕ
38.8
38.9
39.7
40.9
42.7
42.7
43.4
45.5
46.1
47.0
Strength
6.9
6.4
7.8
9.1
8.3
8.8
7.7
9.8
7.3
7.6
МОЕ
48.1
49.2
51.8
62.5
69.9
79.6
80.1
Strength
9.8
7.7
7.6
11.5
11.2
11.7
10.8
Fitting the simple linear regression model to the n =
27 observations on x = modulus of elasticity and y = flexural strength given in the data above resulted in ŷ = 7.595, s;
= 0.186 when x =
40 and ŷ = 9.706,
= 0.263
%3D
for x = 60. The simple linear regression model also resulted in a value of s = 0.9008.
(a) Explain why s; is larger when x = 60 than when x = 40.
The farther x is from x, the smaller the value of
Sỹ.
The farther x is from y, the smaller the value of s;.
The closer x is to x, the smaller the value of
Sỹ.
The closer x is to y, the smaller the value of s,.
(b) Calculate a confidence interval with a confidence level of 95% for the true average strength of all beams whose modulus of elasticity is 40. (Round your answers to three decimal places.)
]) MPa
(c) Calculate a prediction interval with a prediction level of 95% for the strength of a single beam whose modulus of elasticity is 40. (Round your answers to three decimal places.)
MPа
(d) If a 95% CI is calculated for true average strength when modulus of elasticity is 60, what will be the simultaneous confidence level for both this interval and the interval calculated in part (b)?
The simultaneous confidence level for these intervals is at least
%.](https://content.bartleby.com/qna-images/question/fea4cb18-f853-4dd5-87f1-44780e7d8dd9/a68dfec9-16a7-4471-ae0e-31639e05702f/exhw9kk_processed.png)
Transcribed Image Text:Values of modulus of elasticity (MOE, the ratio of stress, i.e., force per unit area, to strain, i.e., deformation per unit length, in GPa) and flexural strength (a measure of the ability to resist failure in bending, in MPa) were
determined for a sample of concrete beams of a certain type, resulting in the following data:
МОЕ
29.9
33.3
33.6
35.4
35.6
36.0
36.3
36.4
37.6
37.6
Strength
6.0
7.1
7.4
6.2
8.2
6.9
6.9
7.7
6.7
6.6
МОЕ
38.8
38.9
39.7
40.9
42.7
42.7
43.4
45.5
46.1
47.0
Strength
6.9
6.4
7.8
9.1
8.3
8.8
7.7
9.8
7.3
7.6
МОЕ
48.1
49.2
51.8
62.5
69.9
79.6
80.1
Strength
9.8
7.7
7.6
11.5
11.2
11.7
10.8
Fitting the simple linear regression model to the n =
27 observations on x = modulus of elasticity and y = flexural strength given in the data above resulted in ŷ = 7.595, s;
= 0.186 when x =
40 and ŷ = 9.706,
= 0.263
%3D
for x = 60. The simple linear regression model also resulted in a value of s = 0.9008.
(a) Explain why s; is larger when x = 60 than when x = 40.
The farther x is from x, the smaller the value of
Sỹ.
The farther x is from y, the smaller the value of s;.
The closer x is to x, the smaller the value of
Sỹ.
The closer x is to y, the smaller the value of s,.
(b) Calculate a confidence interval with a confidence level of 95% for the true average strength of all beams whose modulus of elasticity is 40. (Round your answers to three decimal places.)
]) MPa
(c) Calculate a prediction interval with a prediction level of 95% for the strength of a single beam whose modulus of elasticity is 40. (Round your answers to three decimal places.)
MPа
(d) If a 95% CI is calculated for true average strength when modulus of elasticity is 60, what will be the simultaneous confidence level for both this interval and the interval calculated in part (b)?
The simultaneous confidence level for these intervals is at least
%.
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