Suppose the U.S. president wants an estimate of the proportion of the population

Question

Suppose the U.S. president wants an estimate of the proportion of the population who support his current policy toward revisions in the health care system. The president wants the estimate to be within 0.04 of the true proportion. Assume a 99% level of confidence. The president's political advisors estimated the proportion supporting the current policy to be 0.10. (Use z Distribution Table.)

a. How large of a sample is required? (Round up your answer to the next whole number.)

b. How large of a sample would be necessary if no estimate were available for the proportion supporting current policy? (Round up your answer to the next whole number.) Sample

Explanation / Answer

a)

Note that      
      
n = z(alpha/2)^2 p (1 - p) / E^2      
      
where      
      
alpha/2 =    0.005  
       
      
Using a table/technology,      
      
z(alpha/2) =    2.58  
      
Also,      
      
E =    0.04  
p =    0.1  
      
Thus,      
      
n =    374.4225  
      
Rounding up,      
      
n =    375  

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b)

Note that      
      
n = z(alpha/2)^2 p (1 - p) / E^2      
      
where      
      
alpha/2 =    0.005  
As there is no previous estimate for p, we set p = 0.5.      
      
Using a table/technology,      
      
z(alpha/2) =    2.58  
      
Also,      
      
E =    0.04  
p =    0.5  
      
Thus,      
      
n =    1040.0625  
      
Rounding up,      
      
n =    1041   [ANSWER]

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