CONFIDENCE INTERVALS
Some people are still confused with confidence intervals.
First, is the understanding of what a confidence interval is. As you remember from STA2023
a confidence interval is the interval
computed from the data
that is supposed to capture the
actual population parameter with a
certain level of confidence.
For example the confidence
interval computed based on the sample mean
¯
X
is supposed to capture the population mean
μ
, the confidence interval computed based on the
ˆ
p
is supposed to capture the population
p
.
The confidence level indicates the likeness of the invent to happen. For example
95%
confi
dence interval stands for the following: If we get
100
different samples and get
100
different
estimates that correspond to those samples and produce
100
intervals using those estimates
at least
95
out of the
100
intervals that we produce will capture actual parameter. (This was
the exam question to interpret the confidence interval.)
All confidence intervals look the same:
ESTIMATE
¨
ME
Where
ESTIMATE
is the estimate of the parameter that we compute from the data (like
the sample mean
¯
X
is the estimate of population mean
μ
, the sample proportion
ˆ
p
is the
estimate of the population proportion
p
,
¯
X
1
¡
¯
X
2
is the estimate of the difference between
population means of two groups
μ
1
¡
μ
2
). Parameters of interest are
constants
and they
do not depend on the data in our sample. On the contrary estimates are random and every
sample will give you
different
estimate. For example if I take
100
samples I will get
100
different sample means but we have only one population mean and it is always the same
regardless how many samples I will take. We usually put a “hat” to emphasize that we have
the estimate of the parameter. It will be reasonable to use
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 Summer '08
 TA
 Statistics, Normal Distribution, Standard Deviation, Confidence

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