Assume that 1000 customers are sent a letter telling them to do something.

Further assume that they have two options - to do it, or not to do it.

When modeling that scenario after the fact, to perform analysis, would the following be a fair method:

Obtain the percentage of customers who took action, and assume that this response rate is equivalent to the probability of an individual customer. i.e., if 40 people do it, then assume a 4% probability for a customer to respond.

Then, model the overall picture using a binomial distribution, using that 4% as the basis. I've built a quick graph using those figures, to model the expected response (and find some confidence intervals).

For example, in this case, the probability of 80 customers responding is equal to:

0.04^80 x 0.96^920 x 80C1000

I've then graphed that up, integrated it (really simply), and then calculated the point at which the area under the graph is such that the interval {0,a} has an area of 0.025, and the interval {b,1} has an area of 0.025.

Would I be right in thinking that those variables (a,b) are then the lower and upper limits of my 95% confidence interval?

It's been a while since I did

*real*statistical analysis, and I'm a bit rusty.. any suggestions would be great :o)