lues 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 sam ncrete beams of a certain type, resulting in the following data: MOE 29.7 33.1 33.6 35.2 35.4 36.2 36.2 36.3 37.4 37.8 Strength 5.8 7.1 7.2 6.2 8.0 6.9 7.1 7.7 6.7 6.4 39.7 40.9 42.7 43.6 45.7 MOE 38.6 38.7 42.7 45.9 46.8 Strength 7.1 6.4 8.0 8.9 8.3 8.8 7.9 9.6 7.3 7.6 МОЕ 47.9 49.2 51.6 62.7 69.7 79.6 80.1 Strength 9.8 7.7 7.8 11.5 11.4 11.9 10.6 ting 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 ý = 7.589, s, = 0.180 vwhen x = 40 and ý = 9.749, s, = 0.255 for x = 60. The sim gression model also resulted in a value of s = 0.8718. )Explain why s, is larger when x = 60 than wwhen x = 40. O The closer x is to y, the smaller the value of sp. O The farther x is from x, the smaller the value of sp. The closer x is to x, the smaller the value of sp. O The farther x is from y, the smaller the value of sp. ) 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 ) 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 )Ifa 95% CI is calculated for true average strength when modulus of elasticity is 60, what vill 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 %.
lues 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 sam ncrete beams of a certain type, resulting in the following data: MOE 29.7 33.1 33.6 35.2 35.4 36.2 36.2 36.3 37.4 37.8 Strength 5.8 7.1 7.2 6.2 8.0 6.9 7.1 7.7 6.7 6.4 39.7 40.9 42.7 43.6 45.7 MOE 38.6 38.7 42.7 45.9 46.8 Strength 7.1 6.4 8.0 8.9 8.3 8.8 7.9 9.6 7.3 7.6 МОЕ 47.9 49.2 51.6 62.7 69.7 79.6 80.1 Strength 9.8 7.7 7.8 11.5 11.4 11.9 10.6 ting 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 ý = 7.589, s, = 0.180 vwhen x = 40 and ý = 9.749, s, = 0.255 for x = 60. The sim gression model also resulted in a value of s = 0.8718. )Explain why s, is larger when x = 60 than wwhen x = 40. O The closer x is to y, the smaller the value of sp. O The farther x is from x, the smaller the value of sp. The closer x is to x, the smaller the value of sp. O The farther x is from y, the smaller the value of sp. ) 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 ) 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 )Ifa 95% CI is calculated for true average strength when modulus of elasticity is 60, what vill 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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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
33.1
33.6
35.2
35.4
36.2
36.2
36.3
37.4
37.8
Strength
5.8
7.1
7.2
6.2
8.0
6.9
7.1
7.7
6.7
6.4
МОЕ
38.6
38.7
39.7
40.9
42.7
42.7
43.6
45.7
45.9
46.8
Strength
7.1
6.4
8.0
8.9
8.3
8.8
7.9
9.6
7.3
7.6
МОЕ
47.9
49.2
51.6
62.7
69.7
79.6
80.1
Strength
9.8
7.7
7.8
11.5
11.4
11.9
10.6
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 ý = 7.589, s, = 0.180 when x = 40 and ý = 9.749, s, = 0.255 for x = 60. The simple linear
regression model also resulted in a value of s = 0.8718.
(a) Explain why s, is larger when x = 60 than when x = 40.
O The closer x is to y, the smaller the value of sp.
The farther x is from x, the smaller the value of sp.
O The closer x is to x, the smaller the value of sp.
O The farther x is from y, the smaller the value of sp.
(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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