Sample Size Determination for the Research Project
Statistical Considerations
The first consideration was the amount of sampling error that would be obtained with a
sample. For a sample of 240 it can be calculated as follows.
Sp2 = [ p (1-p) / n ]
p = sample proportion
This numerator will be largest when p = .5 so this will be the maximum error we can
expect.
Sp2 = [ p (1-p) / n ] = [ .5 (1-.5) / 240 ] = .00104
Taking the square root of this: Sp = .03227
z =1.96 for 95% confidence
Consequently, the confidence interval is:
p - zSp ≤ Π ≤ p + zSp
p - 1.96(.03227) ≤ Π ≤ p + 1.96(.03227)
p - .0633 ≤ Π ≤ p + .0633
Thus with this sample size the findings will be within (plus or minus) 6.33% of the true
population proportion. This is useable for most businesses.
Analysis Considerations
The sample size of 240 is large enough to do cross-tabulations with some subgroup
analysis. This sample size will meet our analysis requirements most of the time.
Budget Considerations
Given time and effort constraints each student will only be responsible for two locations
and will get 17-20 responses at each location.
If each student goes to two locations and there are 6-7 students in the research team, then
each research team will go to 12 to 14 locations. If each student distributes 17 to 20
questionnaires then we will have a sample of 14 times 17 = 238 or 12 times 20 = 240 for
our sample size.
In summary when considering statistical, analysis, and budget constraint considerations a
sample size of 240 will meet the needs of the research project.