1 H0 12 22 vs Ha 12 22 with n1 8 n2 7 and 005 critical

1. H₀: ₁² = ₂² vs. H_a: ₁² > ₂², with n₁ = 8, n₂ = 7, and = 0.05

critical region F >_________

2. H₀: ₁ = ₂ vs. H_a: ₁ < ₂, with n₁ = 41, n₂ = 21, and = 0.01

critical region F >______

3.

H₀:

= 1 vs. H_a:

> 1,

with n₁ = 11, n₂ = 18, and = 0.01

critical region F >________

4.

H₀:

= 1 vs.

H_a:

1,

with n₁ = 16, n₂ = 61, and = 0.05

critical region F < ______or F > __________

Solution

1)

degree of fredom numerator: 8-1=7

degree of freedom denominator: 7-1=6

F critical > 4.207

2)

degree of fredom numerator: 41-1=40

degree of freedom denominator: 21-1=20

F critical > 2.695

3)

degree of fredom numerator: 11-1=10

degree of freedom denominator: 18-1=17

F critical > 3.593

4)

degree of fredom numerator: 16-1=15

degree of freedom denominator: 61-1=60

F critical > 1.836 or F < -1.836