Page 299 - Six Sigma Demystified

Part 3 s i x s i g m a to o l s 279

One-Sided Test on Mean: Case 1
Null hypothesis H : m ≥ m 0
0
Alternate hypothesis H : m < m
1 0
Test statistic: t 0

µ
0 t = ( X− )
s/
n
Reject if t < –t
0 α,n–1
One-Sided Test on Mean: Case 2
Null hypothesis H : m ≤ m
0 0
Alternate hypothesis H : m > m 0
1
Test statistic: t
0

µ
0 t = ( X− )
s/
n
Reject if t > t α,n–1
0
Example: H : m ≤ 25; H : m > 25; α = 0.05; n = 25; s = 1.8; X = 25.7
0 1
Test statistic: t = (25.7–25)/(1.8/SQRT(25))=1.94
0
t critical = t 0.05,24 = 1.711

Conclude: Reject H ; true mean m > 25.

0
Hypothesis Tests on One-Sample Mean

Minitab

Menu: Stat\Basic Stats\1 Sample t
Check Perform Hypothesis Test; enter µ .
0
“Options” button: Set Confidence Level 1 – α and alternative Not Equal (two-
sided case) or > or < (for one-sided case).
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