With reference to Exercise 43, use the theory of Exercise 22 to construct a 99% confidence interval for α.
Exercise 43
The following are the scores that 12 students obtained on the midterm and final examinations in a course in statistics:
(a) Find the equation of the least squares line that will enable us to predict a student's final examination score in this course on the basis of his or her score on the midterm examination.
(b) Predict the final examination score of a student who received an 84 on the midterm examination.
Exercises 22
Use the result of part (b) of Exercise 20 to show that
is a value of a random variable having the standard normal distribution. Also, use the first part of Theorem 3 and the fact that 
are independent to show that
is a value of a random variable having the t distribution with n - 2 degrees of freedom.
Exercise 20
Under the assumptions of normal regression analysis, show that
(a) the least squares estimate of α in Theorem 2 can be written in the form
(b) 
has a normal distribution with
Theorem 2
