Reconsider the situation described in Exercise 7, in which x = accelerated strength of c...

Reconsider the situation described in Exercise 7, in which x = accelerated strength of concrete and y = 28-days cured strength. Suppose the simple linear regression model is valid for x between 1000 and 4000 and that β₁ = 1.25 and σ = 350. Consider an experiment in which n = 7, and the x values at which observations are made are x₁ = 1000, x₂ = 1500,x₃ = 2000, x₄ = 2500,x₅ = 3000, x₆ = 3500 and x₇ = 4000.

a. Calculate .

b. What is the probability that the estimated slope based on such observations will be between 1.00 and 1.50?

c. Suppose it is also possible to make a single observation at each of the values are x₁ = 2000, x₂ = 2100,x₁₁ = 3000, . If a major objective is to estimate β1 as accurately as possible, would the experiment with n = 1 be preferable to the one with n= 7?

Reference exercise 7

The article “Some Field Experience in the Use of an Accelerated Method in Estimating 28-Day Strength of Concrete” (J. of Amer. Concrete Institute, 1969: 895) considx ered regressing y = 28-day standard-cured strength (psi) against x = accelerated strength (psi). Suppose the equation of the true regression line is y = 1800 1 1.3x .

a. What is the expected value of 28-day strength when accelerated strength= 2500 ?

b. By how much can we expect 28-day strength to change when accelerated strength increases by 1 psi?

c. Answer part (b) for an increase of 100 psi.

d. Answer part (b) for a decrease of 100 psi.