Suppose candidate A is favored over candidate B by 52 to 48

Suppose candidate A is favored over candidate B by 52% to 48%. A random sample of voters is selected.

A. Determine the minimum sample size needed to insure the probability of an erroneous result would be less than 5%.

B. Determine the minimum sample size needed to insure the probability of an erroneous result would be less than 2%.

You should use Excel and PHstat to perform your analysis. You must completely explain and clearly interpret your analysis, including any computer output that you produce to assist your analysis.

Solution

a)

Candidate A may \"lose\" if the margin of error is greater than 0.02. We need a 95% confidence here.

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 =    0.02  
p =    0.52  
      
Thus,      
      
n =    2397.070304  
      
Rounding up,      
      
n =    2398   [ANSWER]

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b)

Candidate A may \"lose\" if the margin of error is greater than 0.02. We need a 98% confidence here.

Note that      
      
n = z(alpha/2)^2 p (1 - p) / E^2      
      
where      
      
alpha/2 =    0.01  
       
      
Using a table/technology,      
      
z(alpha/2) =    2.326347874  
      
Also,      
      
E =    0.02  
p =    0.52  
      
Thus,      
      
n =    3377.022125  
      
Rounding up,      
      
n =    3378 [ANSWER]