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CONFIDENCE INTERVALS
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CONFIDENCE INTERVALS
Documents prepared for use in course
C22.0103.001
,
New York University, Stern School of Business
The notion of statistical inference
page
3
This section describes the tasks of statistical inference.
Simple estimation
is one form of inference, and confidence intervals are another.
The derivation of the confidence interval
page
5
This shows how we get the interval for the population mean, assuming a
normal population with
known
standard deviation.
This situation is not
realistic, but it does a nice job of laying out the algebra.
Discussion of confidence intervals and examples
page
7
This gives some basic background and then uses illustrations of
confidence intervals for a normal population mean and for a binomial
proportion.
Some examples
page 13
Here are illustrations of intervals for a normal population mean and for a
binomial proportion.
Confidence intervals obtained through Minitab
page 14
Minitab can prepare a confidence interval for any column of a worksheet
(spreadsheet).
Here’s how.
However, Minitab has no special provision
for computing confidence intervals directly from
x
and
s
or, in the
binomial case, from
±
p
.
revised by Avi Giloni Sept 2005
Gary Simon, 2003
Cover photo:
Pansies.
1
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CONFIDENCE INTERVALS
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2
)))))
THE NOTION OF STATISTICAL INFERENCE
)))))
A statistical inference is a quantifiable statement about either a population parameter or a
future random variable.
There are many varieties of statistical inference, but we will
focus on just four of them:
parameter estimation, confidence intervals, hypothesis tests,
and predictions.
Parameter estimation is conceptually the simplest.
Estimation is done by giving a single
number which represents a guess at an unknown population parameter.
If
X
1
,
X
2
, …,
X
n
is a sample of
n
values from a population with unknown mean
µ
,
then we might consider using
X
as an estimate of
µ
.
We would write
µ
=
±
X
.
This is not the only estimate of
µ
, but it makes a lot of sense.
A confidence interval is an interval which has a specified probability of containing an
unknown population parameter.
If
X
1
,
X
2
, …,
X
n
is a sample of
n
values from a population which is assumed to be
normal and which has an unknown mean
µ
, then a 1 
α
confidence interval for
µ
is
X
±
/2;
1
n
s
n
α−
t
.
Here
t
α
/2;
n
1
is a point from the
t
table.
Once the data leads to
actual numbers, you’ll make a statement of the form “I’m 95% confident that the
value of
µ
lies between 484.6 and 530.8.”
A hypothesis test is a yesno decision about an unknown population parameter.
There is
considerable formalism, intense notation, and jargon associated with hypothesis testing.
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This note was uploaded on 05/24/2008 for the course ACC 203 taught by Professor Choi during the Spring '08 term at NYU.
 Spring '08
 CHoi

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