Suppose the US president wants an estimate of the proportion

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 0.03 of the true proportion. Assume a 90% level of confidence. The president\'s political advisors estimated the proportion supporting the current policy to be 0.07. (Use z Distribution Table.)

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

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.)

Solution

A)

Note that      
      
n = z(alpha/2)^2 p (1 - p) / E^2      
      
where      
      
alpha/2 =    0.05  
       
      
Using a table/technology,      
      
z(alpha/2) =    1.644853627  
      
Also,      
      
E =    0.03  
p =    0.07  
      
Thus,      
      
n =    195.7009765  
      
Rounding up,      
      
n =    196   [answer]

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b)

Note that      
      
n = z(alpha/2)^2 p (1 - p) / E^2      
      
where      
      
alpha/2 =    0.05  
As there is no previous estimate for p, we set p = 0.5.      
      
Using a table/technology,      
      
z(alpha/2) =    1.644853627  
      
Also,      
      
E =    0.03  
p =    0.5  
      
Thus,      
      
n =    751.5398484  
      
Rounding up,      
      
n =    752   [ANSWER]