A Gallup poll asked a sample of Canadian adults if they thought the law should a

Question

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 255 people in Quebec, 179 of whom agreed that doctor-assisted suicide should be allowed.

(a) What is the margin of error of the large-sample 99.5% confidence interval for the proportion of all Quebec adults who would allow doctor-assisted suicide?
MoE:

(b) How large a sample is needed to get a ±3 percentage point margin of error (this is very commonly used)? Use the previous sample as a pilot study to get p*.
(You may need four decimal places in your critical value to solve this problem.)
Sample size:  

Explanation / Answer

a)

Note that              
              
p^ = point estimate of the population proportion = x / n =    0.701960784          
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.028643299          
              
Now, for the critical z,              
alpha/2 =   0.0025          
Thus, z(alpha/2) =    2.807033768          
Thus,              

Margin of error = z(alpha/2)*sp =    0.080402708 [ANSWER]

********************

b)

Note that      
      
n = z(alpha/2)^2 p (1 - p) / E^2      
      
where      
      
alpha/2 =    0.0025  
       
      
Using a table/technology,      
      
z(alpha/2) =    2.807033768  
      
Also,      
      
E =    0.03  
p = 179/255 = 0.701960784  
      
Thus,      
      
n =    1831.635395  
      
Rounding up,      
      
n =    1832   [ANSWER]
          

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