Midterm and final examinations in a course in statistics

Reference no: EM131137378

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

Reference no: EM131137378

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