If nothing is known about the p...

ok, i have this question and i'm a quite bit lost because i can't find the rule in my textbook about .5 being substituted. any help would be greatly appreciated. it goes like this...

If nothing is known about the p, 0.5 can be substituted for p in a sample size formula for a population proportion. But when this is done, the resulting sample size may be larger than needed to construct a confidence interval.

Under what circumstances will using p=0.5 in the sample size formula yield a sample size larger than needed to construct a confidence interval for p with a specified bound and a specific confidence interval?

Thank you so much!

The reason for the "rule" is that the maximum variation of a proportion occurs at p=0.5, i.e., p(1-p) is a maximum value of 1/4 then. So you are really using a "worst case" rule for calculating a sample size when you have no idea where the true proportion may lie.

i still don't understand, can someone please help? i have to understand in what case using p = 0.5 in the sample size formula, this p value will give a sample size larger than needed to construct a confidence interval for p with a specified bound and a specified confidence interval.


thank you for your help