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Outline for Confidence Intervals and Tests on One Parameter
R.L. Andrews (revised 10/20/2010)
If the data are from a process first check to assure that the process is stable.
Do not attempt statistical inference
for an unstable process.
Identify the unknown parameter, proportion or mean.
If it is a mean, then determine if
the standard deviation came from the phenomenon or from the sample.
If it is not the sample standard
deviation then one must assume that it is the phenomenon standard deviation.
If you try to find a standard
deviation and cannot find one, then parameter may be a proportion rather than a mean.
I.
Confidence Intervals
for location parameters with 100(1
α
)% confidence.
General form of a 2sided interval for a location parameter:
(
Unbiased Estimator
) ± (
M
argin of
E
rror)
(
Sample based Estimate
) ± (
M
argin of
E
rror)
M
argin of
E
rror [denoted
ME
] = (Table Value)
•
(
S
tandard
E
rror of the estimator [denoted
SE
])
(
Sample based Estimate
) ± (Table Value)•(
S
tandard
E
rror)
The appropriate statistical table and the way the SE value is determined depend on the parameter and
information available.
The table value can be determined by a statistical table (A42&43 or A44) or Excel
function (NORMSINV, NORMINV or TINV).
For the standard normal, the text table A42&43 and Excel
functions use cumulative probability, hence
Z
1
α
denotes a table value with 1
α
area below it and
α
in the upper
tail and
Z
1
α
/2
and 1
α/2
area below and
α/2
in the upper tail.
For the t distribution, the text table E.2 and the
Excel functions use tail probabilities, hence
t
α
denotes a table value with
α
in the upper tail.
t
α
/2
for 2 tail
procedures has
α
=
area in two tails and
α
/2 = the area in one tail.
For 1 tail procedures,
α
is the area in one
tail.
For 1sided intervals only subtract or add the appropriate margin of error to get the appropriate lower or
upper limit.
The "t" distribution table with
∞
degrees of freedom is identical to the standard normal distribution
A.
C.I. for an unknown phenomenon
PROPORTION
, p, with n
•
p
ˆ
>10 & n
•(1
p
ˆ
)>10; where
p
ˆ
is the
sample proportion.
For table values use the standard normal distribution.
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This note was uploaded on 06/20/2011 for the course MGMT 524 taught by Professor Andrews,r during the Spring '08 term at VCU.
 Spring '08
 Andrews,R

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