27.–/2 points Ask Your Teacher My Notes Question Part Points Submissions Used A

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27.–/2 points Ask Your Teacher My Notes Question Part Points Submissions Used 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 264 people in Quebec, 208 of whom agreed that doctor-assisted suicide should be allowed.

(a) What is the margin of error for a 95% confidence interval for the proportion of all Quebec adults who would allow doctor-assisted suicide?

(b) Suppose the researchers wanted a margin of error of 0.01 instead. How large a sample would be needed to achieve this? Use the previous sample as a pilot study to get a value for p^^^.

Explanation / Answer

A)

Note that              
              
p^ = point estimate of the population proportion = x / n =    0.787878788          
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.02516053          
              
Now, for the critical z,              

alpha/2 =   0.025          

Thus, z(alpha/2) =    1.959963985          

Thus,              

Margin of error = z(alpha/2)*sp =    0.049313733 [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 =    0.01  
p =    0.787878788  
      
Thus,      
      
n =    6420.06892  
      
Rounding up,      
      
n =    6421   [ANSWER]

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