A researcher wishes to estimate, with 90% confidence, the population proportion

Question

A researcher wishes to estimate, with 90% confidence, the population proportion of adults who are confident with their country's banking system. His estimate must be accurate within 2% of the population proportion. (a) No preliminary estimate is available. Find the minimum sample size needed. (b) Find the minimum sample size needed, using a prior study that found that 22% of the respondents said they are confident with their country's banking system. (c) Compare the results from parts (a) and (b).

Explanation / Answer

a)

Note that      
      
n = z(alpha/2)^2 p (1 - p) / E^2      
      
where      
      
alpha/2 =    0.025  
As there is no previous estimate for p, we set p = 0.5.      
      
Using a table/technology,      
      
z(alpha/2) =    1.959963985  
      
Also,      
      
E =    0.05  
p =    0.5  
      
Thus,      
      
n =    384.1458821  
      
Rounding up,      
      
n =    385   [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 =    0.05  
p =    0.38  
      
Thus,      
      
n =    362.0190793  
      
Rounding up,      
      
n =    363   [ANSWER]

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c)

When we ahve a prior study, for as long as we get a sample proportion that is not 0.5, we get a smaller target sample size.

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