I want to perform a test to determine (with 95% confidence) whether at least 70% of a population can perform some task.
The test involves sitting a randomly chosen person down and them attempting a task, which they either pass or fail. Equivalently, I flip a weighted coin.
The tests are expensive, so we will only perform a dozen or so of them.
The problem is to calculate pairs of (sample size, number of passes) that would give the required significance.
I want to be able to say something of the form
"Ask 10 people. If 8 or more pass then you can say with 95 confidence that the true ratio in the population is greater than 70%"