Question 1181457
The standard error for population sample proportion is {{{s[e] = sqrt((p(1-p))/n)}}}.

It is initially known that {{{sqrt((p(1-p))/400) = 0.05}}}.

==> {{{(p(1-p))/400 = 0.05^2 = 1/400}}} ===> {{{p(1-p) = 1}}}.

Then from the new requirement of a standard error of 0.025, 

 {{{sqrt((p(1-p))/n) = sqrt(1/n) = 0.025}}}, we get {{{1/n = 0.025^2 = 1/1600}}}, after squaring both sides.


From this we get {{{highlight(n = 1600)}}}.