Page 301 - Six Sigma Demystified

Part 3 s i x s i g m a to o l s 281

X1 − X 2
t =
0 2 2
s s
1 + 2
n 1 n 2
Reject if t > t or t < –t
0 α/2,υ 0 α/2,υ

(s 2 / n + s 2 / n ) 2
where ν = 1 1 2 2
(s 2 / n ) 2 (s 2 / n ) 2
1 1 + 2 2
n 1 −1 n 2 −1

Example: n = 25; X = 15.7; s = 1.8; n = 50; X = 21.2; s = 2.5
1 1 2 2 2
Test statistic: t = 10.90
0
df ν = 63 (always rounded down)

t critical = t 0.025,63 = 2.00

Conclude: Reject H ; means are not equal.
0

Hypothesis Tests on Two-Sample Means

(Assuming Unequal Variances)

Minitab

Menu: Stat\Basic Stats\2 Sample t.
Uncheck Assume Equal Variances.

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

Two-Sided Example at 5% Significance

Two-Sample T Test and Ci
Sample N Mean SD SE Mean
1 25 15.70 1.80 0.36
2 50 21.20 2.50 0.35 (Continued)