A Gallup Poll asked a sample of Canadian adults if they thou

A Gallup Poll asked a sample of Canadian adults if they thought the law should allow doctors to end the life of a patient who is in great pain and near death if the patient makes a request in writing. The poll included 270 people in Quebec, 221 of whom agreed that doctor- assisted suicide should be allowed.

(a) Construct 95% confidence interval for the proportion of all Quebec adults who would allow doctor-assisted suicide? Round your answers to three decimal places.
(b) How large a sample is needed to get the common percentage point margin of error with the same 95% confidence level?

Solution

a)
CI = p ± Z a/2 Sqrt(p*(1-p)/n)))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)=221
Sample Size(n)=270
Sample proportion = x/n =0.819
Confidence Interval = [ 0.819 ±Z a/2 ( Sqrt ( 0.819*0.181) /270)]
= [ 0.819 - 1.96* Sqrt(0.001) , 0.819 + 1.96* Sqrt(0.001) ]
= [ 0.773,0.865]