Section 9.1 – The Logic in Constructing Confidence Intervals
Point Estimate
– A statistic that estimates the true value of a population parameter.
(for example,
“I estimate that the average life span of domestic cats is approximately 10 years”)
x
is the best point estimate of
μ
s is the best point estimate of
σ
p
ˆ
is the best point estimate for
p
Confidence Interval
– A range or interval of values used to estimate the true value of an unknown
population parameter.
(for example,
“I estimate that the average life span of domestic cats is between 9 and 11 years”)
Level of Confidence
– The probability (1 –
α)
100%.
It represents the expected proportion of intervals
that will contain the parameter if a large number of different samples is obtained.
The most common confidence levels:
90%
(.9000)
95%
(.9500)
99%
(.9900)
α
= ________
α
= ________
α
= ________
Critical Value
– A number that separates sample statistics that are likely to occur from those that are
unlikely to occur.
Example
:
Find the critical value corresponding to a 90% confidence level.
90%
α
= _______
α
/
2
= _______
Find
2
α
z
90%
confidence
α
=
α
/
2
=
2
α
z
=
94%
confidence
α
=
α
/
2
=
2
α
z
=
95%
confidence
α
=
α
/
2
=
2
α
z
=
96%
confidence
α
=
α
/
2
=
2
α
z
=
98%
confidence
α
=
α
/
2
=
2
α
z
=
99%
confidence
α
=
α
/
2
=
2
α
z
=
(we will use these in a later section…..)
1
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Margin of Error
(E)
–
A measure of how accurate the point estimate is.
How are confidence intervals created?
Confidence intervals are created by taking the point estimate from your sample and adding and
subtracting the margin of error.
ie,
Point Estimate ± Margin of Error
Notes
:
•As the level of confidence increases, so does the margin of error.
•As the sample size increases, the margin of error decreases.
•The larger the spread in the population, the wider the interval will be.
How to Interpret a Confidence Interval:
• I am __% confident that the true value of
(
μ, ρ, σ
)
is between __ and __.
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 Spring '12
 LisaJuliano
 Logic, Normal Distribution, confidence interval estimate

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