you wish to estimate with 99 confidence the population propo

you wish to estimate with 99% confidence, the population proportion of U.S adults who think that foods containing genetically modified ingredients should be labled. your estimate must be accurate within 2%of the population proportion.

a) no prelimenary estimate is available. find the minimum sample size needed.

b) find the min sample size needed, using a prior study that found that 87% of U.S adults think that food containing genetically modified ingredients should be labled.

c) compare results from part A and B

Solution

A)

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) =    2.575829304  
      
Also,      
      
E =    0.02  
p =    0.5  
      
Thus,      
      
n =    4146.810376  
      
Rounding up,      
      
n =    4147   [ANSWER]

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b)

Note that      
      
n = z(alpha/2)^2 p (1 - p) / E^2      
      
where      
      
alpha/2 =    0.005  
       
      
Using a table/technology,      
      
z(alpha/2) =    2.575829304  
      
Also,      
      
E =    0.02  
p =    0.87  
      
Thus,      
      
n =    1876.017014  
      
Rounding up,      
      
n =    1877   [ANSWER]

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c)

The sample size is lesser when there is a preliminary estimate, as that in part B.