(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.) ]× 7.688 ]× ) MPa 7.528 (c) Calculate a prediction interval vwith 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.) 7.22 •7.005 MPa

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(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 ansvers to three decimal places.)
7.528
]× )*
7.688
MPа
(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.)
7.22
7.995
MPa
Transcribed Image Text:(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 ansvers to three decimal places.) 7.528 ]× )* 7.688 MPа (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.) 7.22 7.995 MPa
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
MOE
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
MOE
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 then = 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.
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 MOE 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 MOE 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 then = 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.
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