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

. 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 doctorassisted 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 + or - 3 percentage point margin of error with the same 95% confidence level?

Solution

A)

Note that              
              
p^ = point estimate of the population proportion = x / n =    0.818518519          
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.023455707          
              
Now, for the critical z,              
alpha/2 =   0.025          
Thus, z(alpha/2) =    1.959963985          
Thus,              
Margin of error = z(alpha/2)*sp =    0.045972341          
lower bound = p^ - z(alpha/2) * sp =   0.772546177          
upper bound = p^ + z(alpha/2) * sp =    0.86449086          
              
Thus, the confidence interval is              
              
(   0.772546177   ,   0.86449086   ) [ANSWER]

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b)

Note that      
      
n = z(alpha/2)^2 p (1 - p) / E^2      
      
where      
      
alpha/2 =    0.025  
       
      
Using a table/technology,      
      
z(alpha/2) =    1.959963985  
      
Also,      
      
E =    0.03  
p =    221/270 = 0.818518519  
      
Thus,      
      
n =    634.0368476  
      
Rounding up,      
      
n =    635   [ANSWER]