Section 8.8 (p.505)

1. Let Y = 1/X, then Y has an F distribution with 8 and 3 degrees of freedom. We have Pr (X > c) = Pr (Y < 1/c) = 0.975 Þ 1/c = 14.54 Þ c = 0.069.

2. Let Y has a t distribution with 8 degrees of freedom, the Y = X² has a F distribution with 1 and 8 degrees of freedom. We have Pr (X > c) = Pr (Y > ) + Pr(Y < ) = 2 Pr (Y > ) = 0.3. Þ =1.108 Þ c = 1.228

6. (1) MLE of s₁² = = S_X²/16 = 7.625. Similarly, MLE of s₂² = S_Y²/10 = 3.96.

(2) Reject H₀ if V ³ 3.01 (F with 15 and 9 df, a=0.05). Here data gives V = = 1.848, we do not reject H₀

7. The random variable has an F distribution with 15 and 9 df. Under the null hypothesis, if s₁² = 3s₂² we have has an F distribution. And we reject H₀ if V ³ c.

9. Let V be as defined as in Exercise 8. When H₀ is true (s₁² = rs₂²), V/r will have an F distribution with 15 and 9 df. And we reject H₀ if V/r < c₁ or V/r > c₂ where c₁ and c₂ are determined as in Exercise 8.