The proportion of public accountants who have changed compan

The proportion of public accountants who have changed companies within the last three years is to be estimated within 4%. The 95% level of confidence is to be used. A study conducted several years ago revealed that the percent of public accountants changing companies within three years was 23. (UseStudent\'s z Distribution Table.) (Round up your answers to the next whole number.)

How many public accountants should be contacted if no previous estimates of the population proportion are available?

Solution

A)

Note that      
      
n = z(alpha/2)^2 p (1 - p) / E^2      
      
where      
      
alpha/2 =    0.025  
       
      
Using a table/technology,      
      
z(alpha/2) =    1.96  
      
Also,      
      
E =    0.04  
p =    0.23  
      
Thus,      
      
n =    425.2171  
      
Rounding up,      
      
n =    426   [ANSWER]

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b)

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) =    1.96  
      
Also,      
      
E =    0.04  
p =    0.5  
      
Thus,      
      
n =    600.25  
      
Rounding up,      
      
n =    601   [ANSWER]