It seems that fzero is having problems with the symbolic part of your function. If you first create it as a separate anonymnous function (using the matlabFunction function):
alp=0.05; x=3; n=25;
syms k a;
nck = matlabFunction(symsum(nchoosek(n,k)*a^k*(1-a)^(n-k+1), k, 0, x-1));
ftest=@(a) 1-alp/2-.5*nchoosek(n,x)*a^x*(1-a)^(n-x) - nck(a);
ZV = fzero(ftest,0.5)
the result is:
ZV =
0.018920195502436
Note that the initial estimate and the result are different, so it is not returning the initial estimate as the optimised result.
