107
5
)
20
)(
58
.
2
(
2
!
¸
¹
·
¨
©
§
!
n
Sample Size Determination for a
Variable- Another Example

Sample Size for Estimating a
Population Proportion
n
p
p
z
E
)
1
(
0
!
where:
n
is the size of the sample
z
is the standard normal value corresponding to
the desired level of confidence
E
is the maximum allowable error
313
2
)
1
(
¸
¹
·
¨
©
§
0
!
E
z
p
p
n
Selecting an Appropriate Sample Size
--
Estimating the Proportion
There are a few options to estimate the proportion
(when it is unknown prior to the sample).
z
Use a Comparable Study.
z
Conduct a Pilot Study.
z
Use the
DEFAULT
value of
0.50
.
–
(0.50) * (0.50) = 0.25
–
(0.40) * (0.60) = 0.24
–
(0.30) * (0.70) = 0.21
–
...
–
(0.01) * (0.99) = 0.0099
313

Example for Sample Size with
Proportions
The American Kennel Club wanted to estimate the proportion of
children that have a dog as a pet.
If the club wanted the
estimate to be within 3% of the population proportion, how
many children would they need to contact?
Assume a 95%
level of confidence and that the club estimated that 30% of the
children have a dog as a pet.
897
03
.
96
.
1
)
70
)(.
30
(.
2
!
¸
¹
·
¨
©
§
!
n
Another Example
A study needs to estimate the
proportion of cities that have private
refuse collectors. The investigator
wants the margin of error to be
within .10 of the population
proportion, the desired level of
confidence is 90 percent, and no
estimate is available for the
population proportion. What is the
required sample size?
cities
69
0625
.
68
10
.
65
.
1
)
5
.
1
)(
5
(.
2
!
!
¸
¹
·
¨
©
§
0
!
n
n

GOALS
1.Define a Point Estimate.
2.DefineLevel of Confidence.
3.
Construct a confidence interval for the population
mean when the population standard deviation is
known.
4.
Construct a confidence interval for a population
mean when the population standard deviation is
unknown.
5.
Construct a confidence interval for a population
proportion.
6.Determine the sample size for attribute and variable sampling.

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- Spring '11
- Leany
- Normal Distribution, Standard Deviation, pilot study, American Management Association