Question

Solve the problem. When performing a hypothesis test for the ratio of two population variances, the upper critical F value is denoted FR. The lower critical F value, FL , can be found as follows: interchange the degrees of freedom, and then take the reciprocal of the resulting F value found in table A-5. FR can be denoted Fα/2 and FL can be denoted F1-α/2. Find the critical values FL and FR for a two-tailed hypothesis test based on the following values: n1 = 9, n2 = 7, α = 0.05

Answer 1

Given that,

= 0.05

/2 = 0.025

1 - (/2) = 0.975

n1 = 9

d.f.1 = n1 - 1 = 9 - 1 = 8

(d.f.1 is degrees of freedom for numerator)

n2 = 7= n2 - 1 = 7- 1 = 6

(d.f.2 is degrees of freedom for denominator)

Use f table.

Fα/2 = F0.025 at d.f.1 = 8 and d.f.2 = 6= 0.215

F1-α/2 = F0.975  at d.f.1 = 8 and d.f.2 = 6= 5.5996

At = 0.05, the critical values are

FL = F(0.975,8, 6) = 0.215

FR = F(0.025, 8, 6) = 5.5996

Answer : (0.215, 5.5996)