q.Name: Jonathan
Who is asking: Parent
Level of the question: Secondary

Question: OK...I am attempting to calculate how my confidence interval will widen at the 95% confidence level if my response universe increases from 100 to 150 or to 200.

There is a universe of 54,000. I take a 5% sample for a test universe of 2,700

If my "yes" universe is 100, at the 95% confidence level, what is my +/- range? (i.e +/- 3? +/-5?)

Historically, 6.6% of the 2,700 you say "yes". I am trying to determine how the confidence interval would change if the number of "yes" responders increased to 150 or to 200.





The confidence limits for the mean of a binomial distribution are

p ± z Sqrt[ p(1 - p)/n]

where p is the proportion of "yes" in the sample, n is the sample size, z is the appropriate number from the normal distribution and Sqrt is square root. For a 95% confidence interval z = 1.96 and and you have a sample size of n = 2,700.

If the number of yes responses in your sample is 100 then p = 100/2700 = 0.037. With these values I get the confidence interval

0.037 ± 0.0071 or 3.7% ± 0.7%

Now change n to 150 and 200 to see how the confidence interval changes.