A research group conducted an extensive survey of 3152 wage

A research group conducted an extensive survey of 3152 wage and salaried workers on issues ranging from relationships with their bosses to household chores. The data were gathered through hour-long telephone interviews with a nationally representative sample. In response to the question, \"What does success mean to you?\" 1649 responded, \"Personal satisfaction from doing a good job.\" Let p be the population proportion of all wage and salaried workers who would respond the same way to the stated question. How large a sample is needed if we wish to be 95% confident that the sample percentage of those equating success with personal satisfaction is within 1.8% of the population percentage? (Hint: Use p 0.52 as a preliminary estimate. Round your answer up to the nearest whole number.)
(Here is the correct answer, I need the solution)

2958 workers

Solution

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 =    0.018  
p =    0.523159898  
      
Thus,      
      
n =    2957.729074  
      
Rounding up,      
      
n =    2958