Size of a telephone survey

What proportion of the population have visited a hospital in the last year?

How many people should be surveyed to be 95% confident that we are within 0.04 of the correct value?

The diagram finds the sample size by a trial-and-error method. For any values of n and p, it finds the width of the resulting confidence interval.

Unknown π
Without a guess at the value of π, drag the slider to 0.5 — the worst-case scenario. (Use the arrow keys for fine adjustment of π.) Then drag the sample size slider and verify that n should be 625 or higher to get the '±' value below 0.04.
We are sure that π will be no higher than 0.10
Verify that a sample size of 225 is now enough to estimate π to within 0.04 with 95% confidence.

Solving an equation

You could also mention that, provided n is reasonably large, the equations can be solved to give