Suppose the President wants an estimate of the proportion of the population who support his current
policy toward gun control. The President wants the estimate to be within .04 of the true proportion.
Assume a 95 percent level of confidence. The President 抯 political advisors estimated the proportion
supporting the current policy to be .60.
a. How large a sample is required?
b. How large a sample would be necessary if no estimate were available for the proportion that
support current policy?
a. Z0.05/2*(p*(1-p)/n)1/2 = 0.04 where p =0.6
Z0.025*(0.24/n)1/2 = 0.04 => 1.96*(0.24/n)1/2 = 0.04
 n = 0.24/(0.04/1.96)2 = 576.24
 so sample size is 576.
b. Let p is estimate proportion, then
Z0.05/2*(p*(1-p)/n)1/2 = 0.04 => 1.96*(p*(1-p)/n)1/2 = 0.04
 n = p*(1-p)/(0.04/1.96)2 = 2401*p*(1-p)
while for p*(1-p), when p=1/2, p*(1-p) arrive maximum and maximum
value is ¼, so n =2401*1/4 =600.25
So if no estimate were available for the proportion that support current
policy, we need 600 sample size.