Section 7.4 (p.397)

3. Since , it follows from equation (6) that

where U has a t distribution with n-1 = 16 degrees of freedom. Note that Pr(U £ 4k) = 1 - Pr(U > 4k) = 0.05. From table of t distribution (p.692), 4 k = -1.746, k = -0.4365.

4. Let , then it has a standard normal distribution. Let , then it has a c² distribution with 3 degrees of freedom. Note also that Y and Z are independent. Therefore, Y/(Z/3)^1/2 has a t distribution. So c = .