An economist wishes to estimate the proportion of household

An economist wishes to estimate the proportion of household income spent on energy (gas, electricity,
and so on), at 95% confidence and to within five percentage points. Assuming no prior knowledge of
the true proportion the minimum sample size needed is about

Solution

We use p=0.5 as estimated.

Given a=1-0.95= 0.05, Z(0.025) = 1.96 (from standard normal table)

So n=(Z/E)^2*p*(1-p)

=(1.96/0.05)^2*0.5*0.5

=384.16

Take n=385