Question

Values of modulus of elasticity (MOE, the ratlo of stress, l.e., force per unit area, to straln, .e., deformation per unit length, in GPa) and flexural strength (a measure of the abllity to resist fallure in bending, In MPa) were determined for a sample of concrete beams of a certain type, resulting in the following data MOF 29.9 33.4 33.6 35.3 35.5 36.2 36.4 36.5 37.5 37.7 38.6 38.9 39.4 41.1 Strength 5.7 7.1 7.1 6.5 8.3 6.8 6.8 7.6 6.76.5 6.963 7.9 9.1 MOE 2.8 3.0 3.3 45.6 46.0 46.8 48.2 19.4 51.6 62.8 70.0 79.3 79.9 Strength 8. 8.6 7.8 9.5 7.2 7.5 9.67.9 7.8 11.4 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 p = 7.540, sy = 0.176 when x = 40 and p = 9.719, s 0.248 for x - 60 (a) Explain why s is larger when x- 60 than when x- 40 The farther x is from x, the smaller the valuc of s The closer x is to x, the smaller the value of s. O O The closer x is to y, the smaller the value of s. The farther x is from y, the smaller the value of sp (b Calculate a confidence interval it a confidence level of 95% for the true average strength of all beams whose modulus of eastict/ 40 ound our answes tot re decimal places. 1.1汀 7.903 MPa a cu ate a prediction interval with a prediction level of 95% for the strength o a single beam w osemodu sofe stic 0. Round your answers s ec ma pla e XMPa d 1 a 95% Cl is calculated or 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 90 96.

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Answer #1

X Value=   40
Confidence Level=   95%
  
Sample Size , n=   27
Degrees of Freedom,df=n-2 =   25
critical t Value=tα/2 =   2.060
X̅ =    45.137
Σ(x-x̅)² =Sxx   4560.123
Standard Error of the Estimate,Se=   0.848
h Statistic = (1/n+(X-X̅)²/Sxx) =    0.043
Predicted Y (YHat)   7.540
  
  
For Individual Response Y  
margin of error,E=t*Se*√(1+h stat) =    1.7841
Prediction Interval Lower Limit=Ŷ -E =   5.756
Prediction Interval Upper Limit=Ŷ +E =   9.324
  

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