Fitting the simple linear regression model to the n = 27 observations on x = modulus of elasticity and y = flexural strength given in Exercise 15 of Section 12.2 resulted in = 7.592, sY^ = .179 when x = 40 and y^ = 9.741, sY^ = .253 for x = 60.
a. Explain why sY ^ is larger when x = 60 than when x = 40.
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.
c. Calculate a prediction interval with a prediction level of 95% for the strength of a single beam whose modulus of elasticity is 40.
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)?