Page 300 - Six Sigma Demystified

280 Six SigMa DemystifieD

Two-Sided Example at 5% Significance

One-Sample T
Test of µ = 25 versus ≠ 25
N Mean SD SE Mean 95% CI T p
25 25.700 1.800 0.360 (24.957, 26.443) 1.94 064
Conclude: Fail to reject (p > 0.05). Samples this extreme occur 6.4 percent
of time. Consider a larger sample.

One-Sided Example at 5% Significance (Case 2, Using Alternative

greater than)
One-Sample T

Test of µ = 25 versus > 25
95% Lower
N Mean SD SE Mean Bound T p
25 25.700 1.800 0.360 25.084 1.94 0.032

Conclude: Reject null (p < 0.05); µ > 25
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(1.94),25–1,2); p = 0.064; fail to reject

One-Sided Example at 5% Significance (Case 2)
=TDIST(ABS(1.94),25–1,1); p = 0.032; reject null

Tests on Two-Sample Means (Assuming Unequal Variances)
Null hypothesis H : m = m
0 1 2
Alternate hypothesis H : m = m 2
1
1
Test statistic: t
0