Fitting the simple linear regression model to the observations on modulus of elasticity and flexural strength given in Exercise 15 of Section 12.2 resulted in when and for . x 5 60 yˆ 5 9.741, s 7.592, sY

ˆ 5 .179 x 5 40 Yˆ 5 .253 yˆ 5 x 5 y 5 n 5 27

a. Explain why is larger when than when .

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)?