Let c 090 s 479 and E 310 What is the minimum sample size

Let c = 0.90, s = 4.79, and E = 3.10. What is the minimum sample size, n, needed to estimate µ? (Assume that s had been found from a preliminary sample that had more than 30 members).

Solution

Note that      
      
n = z(alpha/2)^2 s^2 / E^2      
      
where      
      
alpha/2 = (1 - confidence level)/2 =    0.05  
      
Using a table/technology,      
      
z(alpha/2) =    1.644853627  
      
Also,      
      
s = sample standard deviation =    4.79  
E = margin of error =    3.1  
      
Thus,      
      
n =    6.459548342  
      
Rounding up,      
      
n =    7   [ANSWER]