Seminar aus Statistik für das Magisterstudium - Example 5.1/5.2
The prevalence rate of a disease among children in a particular area is believed to be about 30%. How many subjects are required if we wish to determine this prevalence to within about 3 percentage points with 95% confidence that this is true?
> # calculates n for a given confidence interval width > power.binom.conf.int = function(prob, conf.int.width, alpha=.05) + 4*qnorm(1-(alpha/2))^2 * prob * (1-prob) / conf.int.width^2 > > power.binom.conf.int(0.3, 0.03)  3585.362
Suppose all that is known about the prevalence of the disease is that it might be somewhere between 10% and 40%. How does this effect the sample size calculation described in Example 5.1?