Margin of error = Confidence coefficient*Standard error of p
Margin of error = 0.009
Confidence coefficient is the critical value of z for 99% confidence level = 2.575
Standard error of p = sqrt [p*(1-p)/n]
= sqrt [0.5*0.5/n]
= 0.5/sqrt n
[when p value is not known, it shall be taken equal to 0.5 because the standard error of p is maximum at that level]
Therefore,
0.009 = 2.575*0.5/sqrt n
n = [2.575*0.5/0.009]^2 = 20465
Sample size = 20,465