Formulas for Proportions
Confidence Interval for
π
(proportion):
/ 2
(1
)
p
p
p
z
n
α

±
1.
The sample proportion,
p
, estimates the population mean,
π
, and for large enough samples this
interval is sufficient.
2.
The margin of error is made of:
a.
z
α
/2
gives us the desired confidence level.
b.
the
standard error
of
p
is
(1 )
p
p p
SE
n

=
since the standard deviation is dependent on
π
, the parameter
we’re having to estimate.
c.
the sample size,
n
, which allows us to control the variability of our statistic,
p
.
3.
We must have a random sample so
p
is unbiased and the standard deviation of
p
is
(1
)
n
π

.
4.
We are using
z
scores, so we must have
n
π
and
n
(1
π
)
≥
10.
Since we don’t know
π
, we need
np
and
n
(1

p
)
≥
10.
When testing the proportion:
H
0
:
π
=
π
0
vs. H
A
:
π
≠
π
0
The TS:
0
0
0
(1
)
p
z
n

=

Since we have a hypothesized value for
π
, we use this value in our test statistic.
Two sample cases:
Confidence Interval for
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