Question

Find the critical value of the chi-square distribution for each of the following situations:

1. H_A: σ² > 0.25, n = 10, α = 0.05
2. H_A: σ² > 20, n = 20, α = 0.025
3. H_A: σ² ≠ 0.25, n = 10, α = 0.10

Answer 1

a)

Ha: > 0.25

This is right tailed test.

df = n - 1 = 10 - 1 = 9

From chi-square critical value table,

Chi-square critical value = 16.919

b)

Ha: > 20

This is right tailed test.

df = n - 1 = 20 - 1 = 19

From chi-square critical value table,

Chi-square critical value = 32.852

c)

Ha: 0.25

This is two tailed test.

df = n - 1 = 10 - 1 = 9

From chi-square critical value table,

Chi-square critical value = L = 3.325 , U = 16.919