Question

Consider testing H0: σ²₁ ≤ σ²₂ vs. Ha: σ²₁ > σ²₂ given that ?₁ = 25, s²₁  = 7.4, ?₂ = 31, s²₂ = 6.2.

a) Calculate the value of the test statistic, F*.

b) Test the hypothesis at the 0.025 level of significance, using the classical approach.

Critical region:

c) Decision:

d) Reason:

Answer 1

Solution:

a)

The test statistic is

F^* = s₁²/s₂² = 7.4/ 6.2 = 1.19

F^* = 1.19

b)

> sign in Ha indicates that the test is "right tailed"

Critical value in this case is F _{, df1,df2}

d.f.₁ = n₁ - 1 = 25 - 1 = 24

_d.f.2 = n₂ - 1 = 31 - 1 = 30

= 0.025

So , critical value is F_0.025,24,30 = 2.14

Critical region: > 2.14

c)

Decision: Fail to reject H₀

d)

Because Test statistic 1.19 do not fall in critical region (i.e. 1.19 is not greater than 21.14)