Suppose the US president wants an estimate of the proportion

Suppose the U.S. president wants an estimate of the proportion of the population who support his current policy toward revisions in the Social Security system. The president wants the estimate to be within 0.022 of the true proportion. Assume a 99 percent level of confidence. The president\'s political advisors estimated the proportion supporting the current policy to be 0.57. (Round up your answers to the next whole number.)

(a) How large of a sample is required? .

(b) How large of a sample would be necessary if no estimate were available for the proportion that support current policy?

Solution

Suppose the U.S. president wants an estimate of the proportion of the population who support his current policy toward revisions in the Social Security system. The president wants the estimate to be within 0.022 of the true proportion. Assume a 99 percent level of confidence. The president\'s political advisors estimated the proportion supporting the current policy to be 0.57. (Round up your answers to the next whole number.)

P=0.57

For 99%, z=2.576

d=0.022

Sample size = (z²*p*(1-p))/d²

= (2.576²*0.57*0.43)/0.022²

=3360.39

The sample size required= 3361

( some software gives 3360 as the final answer because they use z value as 2.5758)

(b) How large of a sample would be necessary if no estimate were available for the proportion that support current policy?

we assume P=0.5

For 99%, z=2.576

d=0.022

Sample size = (z²*p*(1-p))/d²

= (2.576²*0.5*0.5)/0.022²

=3427.57

The sample size required= 3428