Determine the critical region and critical values that would

Determine the critical region and critical value(s) that would be used to test the following hypotheses using the classical approach when F is used as the test statistic.

(a)

H₀: ₁² = ₂² vs. H_a: ₁² > ₂²,

with n₁ = 8, n₂ = 7, and = 0.05

critical region F >_______

(b)

H₀:

₁²/₂² = 1 vs.

H_a:

                                                    ₁²/₂² 1,

with n₁ = 16, n₂ = 61, and = 0.05

critical region F < ________or F > ______

(c)

H₀:

                                                ₁^2/₂²= 1 vs.

H_a:

                                                     ₁²/₂² > 1,

with n₁ = 11, n₂ = 18, and = 0.01

critical region F >_______

(d)

H₀: ₁ = ₂ vs. H_a: ₁ < ₂,

with n₁ = 41, n₂ = 21, and = 0.01

critical region F >___________

Solution

a) Critical F >4.205

b) F<-1.8365 or F>1.8365

c) F>3.592

d) F>2.695