One-Sided Confidence Intervalgchang.people.ysu.edu/class/mph/note/06_5_CI_OneSidedCI.pdf ·...
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One-Sided Confidence Interval
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Size of Interval
95% Samples95% Samples
σσxx__
⎯⎯XX
µµ+1.96+1.96σσ⎯⎯xxµµ--1.961.96σσ⎯⎯xx
µµ
0.0250.025
.95
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Two-Sided C. I.
Z C.I.:
t C.I.:
) , ( 2/2/ nsZX
nsZX ⋅+⋅− αα ) , ( 2/2/ n
sZXnsZX ⋅+⋅− αα
) , ( 2/2/ nstX
nstX ⋅+⋅− αα ) , ( 2/2/ n
stXnstX ⋅+⋅− αα
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One-Sided C. I.
Z C.I.:Lower interval Upper interval
t C.I.:Lower interval Upper interval
) , (n
sZX ⋅+∞− α ) , (n
sZX ⋅+∞− α
) , ( ∞⋅−n
sZX α ) , ( ∞⋅−n
sZX α
),( nstX ⋅+∞− α ),( nstX ⋅+∞− α
),( ∞⋅−nstX α ),( ∞⋅−nstX α
Upper bound
Lower bound Upper bound
Lower bound4
Lower Interval
95% Samples95% Samples
σσxx__
⎯⎯XX
µµ++1.641.64σσ⎯⎯xx
µµ
0.05
.95
zα = z.05
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Upper Interval
95% Samples95% Samples
σσxx__
⎯⎯XXµµ--1.641.64σσ⎯⎯xx
µµ
0.05
.95
zα = z.05
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Estimation Example Mean (n > 30)
The mean of a random sample of n = 100 is⎯x = 50, with s = 10. Set up a upper 95% confidence interval estimate for µ.
) , 36.48 (
) , 1001064.150 (
) , (
1.64. z .05, ,95.1
∞
∞⋅−
∞⋅−
===−
nsZX α
ααα
) , 36.48 (
) , 1001064.150 (
) , (
1.64. z .05, ,95.1
∞
∞⋅−
∞⋅−
===−
nsZX α
ααα
