Posted after class
WEEK 10 – Wed, Nov 3
Correct Formulas for SampleSize Determination
The equations that should be solved when using simple random sampling from a
population of size N are
n
N
n
N
z
B
σ
α
1
2
/


=
(*)
n
p
p
N
n
N
z
B
)
1
(
1
2
/



=
(**)
with results
1
/
/
2
2
2
2
/
2
2
2
2
/

+
=
B
z
N
B
N
z
n
c
(610c)
1
/
)
1
(
/
)
1
(
2
2
2
/
2
2
2
/


+

=
B
p
p
z
N
B
N
p
p
z
n
c
(611c)
where we have chosen to label the
correct
sample size as
n
c
.
There is a better way to
state these results
: To evaluate (610c) or (611c), first calculate
n
b
using the book’s (6
10) or (611) and then plug the result into (***).
N
n
n
n
b
b
c
)
1
(
1

+
=
.
(***)
1
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View Full DocumentExample
.
CI estimation of µ.
Suppose the population size is N = 854, σ is unknown,
desired margin of error is B = 2, and desired confidence level is 99%.
Suppose σ = 10 is
used for planning the sample size
.
We use (610c).
We find
n
b
= 165.89 and then by
(***) we find
n
c
= 139.1.
This suggests that the sample size should be
n
= 140 for a
simple random sample selected from the population of size N = 854.
Hypothetical Implementation.
Take
n
= 140 and use the tinterval estimate of µ with
139
df
once the data are in.
Using the book’s Table 3 and the conservative approach to
finding the tmultiplier t
.005
, we would use the multiplier t
.005
= 2.617 (120
df
).
With
some hypothetical data
x
= 76.4, s = 10.3, the tinterval estimate for the population
mean µ is
)
140
/
3
.
10
(
1
854
140
854
617
.
2
4
.
76
/
1
005
.

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 Spring '08
 Anderson
 NC

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