he proportion of public accountants who have changed compani

he proportion of public accountants who have changed companies within the last three years is to be estimated within 4%. The 90% 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 22.

(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 =    0.05  
       
      
Using a table/technology,      
      
z(alpha/2) =    1.645  
      
Also,      
      
E =    0.04  
p =    0.22  
      
Thus,      
      
n =    290.2211813  
      
Rounding up,      
      
n =    291   [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) =    1.645  
      
Also,      
      
E =    0.04  
p =    0.5  
      
Thus,      
      
n =    422.8164063  
      
Rounding up,      
      
n =    423   [ANSWER]