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## Lecture 8 Part II.pdf Page 1 2 3 4 5 6 7 8 9 10 11 12

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Confidence Intervals

Sample Size

•  Assumptions
–

Population Standard Deviation Is Known

–

Population Is Normally Distributed

–

If Not Normal, use large samples

Too Big:
•  Requires too
much resources

Too Small:
•  Won t do
the job

•  Confidence Interval Estimate

X − Z1−α / 2 ⋅

σ
n

≤ µ ≤ X + Z1−α / 2 ⋅

σ
n
25

Example: Sample Size for Mean

Factors Affecting
Interval Width
•  Data Variation
•

measured by σ

27

What sample size is needed to be 90% confident
of being correct within ± 5? A pilot study
suggested that the standard deviation is 45.

Intervals Extend from
X ! Z &quot;! X a X + Z &quot;! X

X

(+\- 5 is the margin of error, i.e.,
the width of the interval)

•  Sample Size

σX =σX / n

n =#

•  Level of Confidence
(1 - α)

Z 2σ#2
5

2

=#

1.645
5

2
2

45

2

=# 219.2 ≅# 220
Round Up

© 1984-1994 T/Maker Co.

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