Page 303 - Six Sigma Demystified

Part 3 s i x s i g m a to o l s 283

11 4 .
0 t = 2 1 . / 25 = 27 14
.

t critical = t 0.025,24 = 2.064
Conclude: Reject H ; means are not equal.
0

Hypothesis Tests on Paired Means

Minitab

Menu: Stat\Basic Stats\Paired t
“Options” button: Set Confidence Level 1 – α and alternative Not Equal (two-
sided case) or > or < (for one-sided cases).

Paired T Test and Ci
N Mean SD SE Mean
Difference 25 11.400 2.100 0.420
95% CI for mean difference: (10.533, 12.267)

T test of mean difference = 0 (versus not): T value = 27.14; p value = 0.000.
Conclude: Reject null (p < 0.05); means are not equal.
Excel

Calculate p as

Two-sided: TDIST(|t |,n-1,2)

0
One-sided Case 1: 1-TDIST(|t |,n-1,1) for t > 0; TDIST otherwise
0
0
One-sided Case 2: TDIST(|t |,n-1,1) for t > 0; 1-TDIST otherwise
0
0
Two-Sided Example at 5% Significance
=TDIST(ABS(27.14),24,2); p = 0.000; reject null; means are not equal.

Tests on One-Sample Variance

Two-Sided Test on Variance
Null hypothesis H : σ = σ 2
2
0 1 0
Alternate hypothesis H : σ ≠ σ 2 0
2
1
1