suppose you wish to estimate a binomial parameter p correct

suppose you wish to estimate a binomial parameter p correct to within .04,with probaility equal to .95. if you suspect that p is equal to some value between .1 and .3 and you want to be certain that your samole is large enough, how large should n be? (HINT: when calculating the standared error, use the vaule of p in the interval .1<p<.3 that will give the largest sample size.)

Solution

Compute Sample Size ( n ) = n=(Z/E)^2*p*(1-p)
Z a/2 at 0.05 is = 1.96
Samle Proportion = p is equal to some value between .1 and .3 = 0.3 [ To be large enough sample size n, larger vealue considered ]
ME = 0.04
n = ( 1.96 / 0.04 )^2 * 0.3*0.7
= 504.21 ~ 505