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.

Thanks!

Jonathan

Jonathan,

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.

Penny