Page 101 - Design for Six Sigma for Service (Six SIGMA Operational Methods)

82 Chapter Four

Example 4.6
In a survey study of household incomes for county Y, the preliminary estimate
of average household income is $40,000 and the standard deviation is estimated
to be $6000. If we would like to determine a survey sample size so that the
margin of error for the average household income is no more than $1000, what
is the minimum sample size, if a confidence level of 95% is desired?
Using Eq. (4.9),

Z s 2 1 96 2 × 6000 2
2
.
n = a = = 139
∆ 2 m 1000 2
Therefore, a minimum sample size of 139 households is required.
Determination of Sample Size for Interval-Scale Variables When the
Population Is Small
The sample size rule specified by Eq. (4.9) is based on the assumption that
the population size is infinite or very large. In some survey studies,
however, the population size is rather limited. If the population size, say
N, is known, then according to Rea and Parker (1992), the sample size n
can be calculated by

Z 2 s 2
n = a/2 (4.10)
∆ 2 m + Z a/2 s 2 ( N − )1
2
Example 4.7
In a survey study of household incomes for county Y, the preliminary estimate
of average household income is $40,000 and the standard deviation is estimated
to be $6000. If we would like to determine a survey sample size so that the
margin of error for the average household income is no more than $1000, and
it is known that the total number of households in county Y is 5000, what is the
minimum sample size, if a confidence level of 95% is desired?

By using Eq. (4.10)
Z s 2 2 2
2
n = a /2 = . 1 96 × 6000 = 135
∆ 2 m + Z s 2 ( N − )1 1000 2 + (.1 96 2 × 6000 2 ) 4999
2
a /2