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115
Lecture 12:
CHAPTER 5: CONFIDENCE INTERVALS
LargeSample Confidence Intervals for a
Population Mean – Cont’d (Section 5.1, page 323)
Recall:
Last class, we took a look at the most common confidence
intervals:
Summary
Other Confidence Levels
Note:
Other commonly used large sample confidence intervals for a
population or process mean
are given below:
Let
n
X
X
,...,
1
be a
large
)
30
(
n
random sample from a
population with mean
and standard deviation
, so that
x
is
approximately normal.
Then a level
)%
1
(
100
two sided
confidence interval for
is
x
z
x
2
where
n
x
.
When the value of
is unknown, it can be
replaced with the sample standard deviation
s
.
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There are two methods for finding the critical value (i.e.,
2
z
):
117
Example:
The sample mean and standard deviation for the fill
weights of 100 boxes are
05
.
12
x
and
1
.
0
s
.
Find an 85%
confidence interval for the mean fill weight of the boxes.
Example:
In a sample of 50 microdrills drilling a lowcarbon alloy
steel, the average lifetime (expressed as the number of holes drilled
before failure) was 12.68 with a standard deviation of 6.83.
An
engineer reported a confidence interval of (11.09, 14.27) but
neglected to specify the level.
What is the level of this confidence
interval?
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Determining the Sample Size Needed for a Confidence Interval of
Specified Width
The halfwidth 1.96
n
s
of the 95% CI is sometimes called the bound
on the error of estimation associated with a 95% confidence level;
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This note was uploaded on 06/20/2011 for the course STAT 2800 taught by Professor Paula during the Winter '11 term at UOIT.
 Winter '11
 Paula

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