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 resistfailure in bending, in MPa) were determined for a sample ofconcrete beams of a certain type, resulting in the following data:MOE 29.9 33.4 33.6 35.3 35.4 36.2 36.3 36.5 37.7 37.9 38.6 38.839.7 41.2 Strength 6.0 7.1 7.3 6.1 8.0 6.6 6.8 7.7 6.7 6.7 7.0 6.58.1 8.8 MOE 42.8 42.8 43.4 45.8 45.8 47.0 48.1 49.2 51.8 62.6 69.979.6 80.2 Strength 8.3 8.8 8.0 9.6 7.6 7.5 9.7 7.7 7.5 11.6 11.511.8 10.9 Fitting the simple linear regression model to the n = 27observations on x = modulus of elasticity and y = flexural strengthgiven in the data above resulted in ? = 7.576, sy hat = 0.178 whenx = 40 and ? = 9.777, sy hat = 0.251 for x = 60. (a) Explain why syhat is larger when x = 60 than when x = 40. The closer x is to x,the smaller the value of sy hat. The farther x is from y, thesmaller the value of sy hat. The farther x is from x, the smallerthe value of sy hat. The closer x is to y, the smaller the value ofsy hat. (b) Calculate a confidence interval with a confidence levelof 95% for the true average strength of all beams whose modulus ofelasticity is 40. (Round your answers to three decimal places.) ,MPa (c) Calculate a prediction interval with a prediction level of95% for the strength of a single beam whose modulus of elasticityis 40. (Round your answers to three decimal places.) , MPa (d) If a95% CI is calculated for true average strength when modulus ofelasticity is 60, what will be the simultaneous confidence levelfor both this interval and the interval calculated in part (b)? Thesimultaneous confidence level for these intervals is at least