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 33.6 35.4 35.6 36.2 36.2 36.3 37.4 37.8 Strength 5.6 7.3 7.2 6.2 8.0 6.9 6.9 7.5 6.9 6.4 MOE 38.7 38.E 39.7 41.1 42.9 42.9 43.4 45.7 45.9 47.0 Strength 7.1 6,4 7.8 9.1 B.6 7.7 9.6 7.3 7.6 MOE 47.9 49.4 51.6 62.5 69.7 79.4 79.9 Strength 9.1 7.7 7.8 11.5 11,4 11.7 10.0 Fitting the simple linear regression model to the n = 27 observations on * = modulus of elasticity and y = flexural strength given in the data above resulted In ? = 7.566, s. = 0.178 when x = 40 and / = 9.742, s; = 0.252 for x = 60. The simple linear regression model also resulted in a value of s = 0.8596. (a) Explain why so is larger when x = 60 than when x = 40, The closer x is to y, the smaller the value of s. The farther x is from x, the smaller the value of The closer x is to x, the smaller the value of s;. The farther x Is from y, the smaller the value of sp- (b) Calculate a confidence interval with a confidence level of 959% 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 950% for the strength of a single beam whose modulus of elasticity is 40. (Round your answers to three decimal places.) MP# (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