An article in Concrete Research presented data on compressive strength x and intrinsic permeability y of various concrete mixes and cures. Summary quantities are n = 14, Σ y i = 572, = 23,530, Σ x i =...

An article in
Concrete Research
presented data on compressive strength
x
and intrinsic permeability
y
of various concrete mixes and cures. Summary quantities are
n
= 14, Σy

_i
= 572,
= 23,530, Σx

_i
= 43,
= 157.42, and Σx

_i

y

_i
= 1697.80. Assume that the two variables are related according to the simple linear regression model. on
y
= intrinsic permeability of concrete and
x
= compressive strength. Find a 95% confidence interval on each of the following:

(a) Slope

(b) Intercept

(c) Mean permeability when
x
= 2.5

(d) Find a 95% prediction interval on permeability when
x
= 2.5. Explain why this interval is wider than the interval in part (c).