Page 304 - Six Sigma Demystified

284 Six SigMa DemystifieD

Test statistic:
s 2
2
χ = (n − 1)
0
σ 2
0
Reject if χ > χ 2 or χ < χ 2
2
2
0 α/2,n-1 0 α/2,n-1
Example: H : σ = 25; H : σ ≠ 25; α = 0.05; n = 15; s = 23
2
2
2
1
1
1
0
2
Test statistic: χ = (15 – 1)/(23/25)
0
=12.88
χ 2 0.975,14 = 5.629; χ 2 0.025,14 = 26.119

Conclude: Fail to reject H .
0
One-Sided Test on Variance: Case 1
Null hypothesis H : σ ≥ σ 2
2
0 1 0
Alternate hypothesis H : σ < σ 2 0
2
1
1
Test statistic:
s 2
χ = (n − 1)
2
0
σ 2
0
Reject if χ < χ 2 1-α/2,n-1
2
0
2
Example: H : σ ≥ 25; H : σ < 25; α = 0.05; n = 15; s = 23
2
2
0 1 1 1
2
Test statistic: χ = (15 – 1)/(23/25)
0
=12.88

χ 2 0.95,14 = 6.571; χ 2 0.05,14 = 23.685
Conclude: Fail to reject H .
0
One-Sided Test on Mean: Case 2
Null hypothesis H : σ ≤ σ 2
2
0 1 0
Alternate hypothesis H : σ > σ 2 0
2
1
1
Test statistic:
s 2
2
χ = (n − 1)
0
σ 2
0
Reject if χ > χ 2 α,n-1
2
0