Page 306 - Six Sigma Demystified

286 Six SigMa DemystifieD

Test on Two Sample Variances
Two-Sided Test on Two Variances
Null hypothesis H : σ = σ 2
2
0 1 2
Alternate hypothesis H : σ < σ 2 2
2
1
1
Test statistic: F
0
s 2
F = s 1 2 2
0
where s > s .
1 2
Reject if F > F α/2,ν1,ν2 , where ν = n – 1; ν = n – 1; equal n not required.
1
0
1
2
2
Example: Using a 90% confidence level with n = 50; S = 2.5;
1
1
n = 25; S = 1.8
2
2
Test statistic:
.
2 5 2
F = = 1 93
.
0 2
1 8
.
ν = 50 – 1 = 49; ν = 25 – 1 = 24

1

2
F = 1.86 [using Excel FINV(0.05,49,24)]
0.05,49,24
Conclude: Reject H ; variances are not equal.
0
One-Sided Test on Two Variances:
Null hypothesis H : σ ≥ σ 2 2
2
0
1
Alternate hypothesis H : σ < σ 2
2
1 1 2
Test statistic: F 0
F = s 1 2
0 s 2
2
where s > s .
1 2
Reject if F > F α,ν1,ν2 , where ν = n – 1; ν = n – 1; equal n not required.
2
2
1
0
1
Hypothesis Tests on Two-Sample Variances
Minitab
Menu: Stat\Basic Stats\2 Variance
Reports two-sided case.