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:
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:
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Please answer all parts
![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:
MOE
29.7
33.3
33.8
35.4
35.4
36.0
36.3
36.4
37.6
37.6
Strength
5.8
7.3
7.2
6.4
8.2
6.7
6.9
7.7
6.9
6.6
МОЕ
38.6
38.7
39.5
41.1
42.7
42.9
43.6
45.7
45.9
46.8
Strength
6.9
6.4
8.0
9.1
8.1
8.8
7.9
9.8
7.3
7.6
MOE
47.9
49.2
51.6
62.7
69.9
79.4
80.1
Strength
9.6
7.7
7.8
11.7
11.4
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 = 7.608, s, = 0.183 when x = 40 and ŷ = 9.768, s, = 0.259 for
x = 60. The simple linear regression model also resulted in a value of
s = 0.8851.
(a) Explain why so is larger when x = 60 than when x = 40.
O The closer x is to x, the smaller the value of so.
O The farther x is from y, the smaller the value of so.
O The closer x is to y, the smaller the value of so.
O The farther x is from x, the smaller the value of sọ.
(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.)
MPa
(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
%.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fda5cf1ef-ed5b-45b4-b720-27437f28fd1b%2Fd08257b5-33d1-4bb8-b21e-b521437afd63%2Fj0chj6f_processed.jpeg&w=3840&q=75)
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:
MOE
29.7
33.3
33.8
35.4
35.4
36.0
36.3
36.4
37.6
37.6
Strength
5.8
7.3
7.2
6.4
8.2
6.7
6.9
7.7
6.9
6.6
МОЕ
38.6
38.7
39.5
41.1
42.7
42.9
43.6
45.7
45.9
46.8
Strength
6.9
6.4
8.0
9.1
8.1
8.8
7.9
9.8
7.3
7.6
MOE
47.9
49.2
51.6
62.7
69.9
79.4
80.1
Strength
9.6
7.7
7.8
11.7
11.4
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 = 7.608, s, = 0.183 when x = 40 and ŷ = 9.768, s, = 0.259 for
x = 60. The simple linear regression model also resulted in a value of
s = 0.8851.
(a) Explain why so is larger when x = 60 than when x = 40.
O The closer x is to x, the smaller the value of so.
O The farther x is from y, the smaller the value of so.
O The closer x is to y, the smaller the value of so.
O The farther x is from x, the smaller the value of sọ.
(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.)
MPa
(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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