Reconsider the situation described in Exercise 7, in which x = accelerated strength of concrete and y = 28day cured strength. Suppose the simple linear regression model is valid for x between 1000 and 4000 and that β1 = 1.25 and ( = 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 ( 1, the standard deviation of 1.
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 n = 11 values x1 = 2000, x2 = 2100,..., x11 = 3000. If a major objective is to estimate β1 as accurately as possible, would the experiment with n = 11 be preferable to the one with n = 7?