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LECTURE SYSTEMS 12
CONFIDENCE INTERVALS Quality Control Charts Sample Design Problem ONE-SIDED INTERVALS Pollution Example Critical Confidence Levels For next time: Devore, Sections 7.2.-7.3 (omit 7.4)
CONFIDENCE INTERVALS
Given the probability interval for X n in terms of : (1)
Pr za / 2
(
n
X n + za / 2
n
) = 1
observe that since (2)
za / 2
n
X n + za / 2
n
n n
X n za / 2
X n + za / 2
we obtain the equivalent confidence interval for in terms of X n as (3)
Pr X n za / 2
(
n
X n + za / 2
n
) = 1
This is also written as:
X n za / 2
n
= 100(1 )% confidence interval for
GENERAL PROCEDURE FOR TWO-SIDED INTERVALS
(1) Choose Level [Confidence 1 ]: (2) Determine Standard Error (3) Conclude that:
X n za / 2
n
( )
n
n
X n + za / 2
with 100(1 )% confidence. TYPICAL VALUES: Conf. Level strong standard weak 99% 95% 90%
Level
.01 .05 .10
z Value
2.58 ( z.005 ) 1.96 ( z.025 ) 1.65 ( z.05 )
SAMPLE DESIGN PROBLEM
For any given maximal deviation, , and confidence level, 100(1 ) , what is the smallest sample size, n which will ...