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BUAD 310
Applied Business Statistics
2/8/10
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View Full Document A Quick Review
Estimation
of population parameters (
e.g., population mean μ
and population proportion
p
)
•
Point estimate:
one number estimate such as the sample
mean
and the sample proportion
The sampling distributions of
and
:
approximately
normal
•
Interval estimate:
confidence interval (CI)
2
Confidence Interval
CI: an interval of likely estimates that contains the true
value of the population parameter which is unknown to
us with a given confidence level.
E.g., in the gas mileage case the mean mpg for a sample of
n
=49 selected cars is
, and the sample std dev
s
=0.7992. What can we say about the true mean mpg μ
based on this sample information?
•
You are certainly 100% confident that μ > 0.
•
Then how confident are you that µ ≥ 31?
Idea: construct a
(1α)100% CI
for μ of the form
point
estimate
±
margin of error
(e.g.,
)
3
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View Full Document Confidence Level
What does the confidence level of a CI (e.g., 95%) mean?
•
Like sample mean, CI changes from sample to sample.
•
95% means that for the population of all possible CI’s
constructed in a given way, there is 95% probability that the
true value (e.g., μ) falls in the CI.
4
Confidence Interval vs Tolerance Interval
•
CI
bounds a population parameter (e.g., mean) with some
confidence, while
TI
gives a range of individual measurements
in a population that represents a specified proportion of the
population.
(Recall the empirical rule gives three tolerance
intervals:
68.26% TI [
¹

s
,
¹
+
],
95.44% TI [
¹
2
,
¹
+2
],
99.73% TI [
¹
3
,
¹
+3
]
)
•
CI
characterizes the behavior of the average, while
TI
characterizes the behavior of a range of individuals.
5
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View Full Document CI for a Population Mean with Known
σ
6
If sampled population has mean μ
and
known
σ, a
(1α)100%
confidence interval
for μ is
Note
:
this formula for CI will not
work if the sample size is
small
(e.g., n<30)
and
the data is
not
normal
.
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This note was uploaded on 09/05/2010 for the course BUAD 310 taught by Professor Lv during the Spring '07 term at USC.
 Spring '07
 Lv
 Business

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