A population is estimated to have a standard deviation of 15

A population is estimated to have a standard deviation of 15. We want to estimate the population mean within 4, with a 98% level of confidence. (Use z Distribution Table.)

How large a sample is required? (Round up your answer to the next whole number.) Sample required is .

Solution

Note that      
      
n = z(alpha/2)^2 s^2 / E^2      
      
where      
      
alpha/2 = (1 - confidence level)/2 =    0.01  
      
Using a table/technology,      
      
z(alpha/2) =    2.33  
      
Also,      
      
s = sample standard deviation =    15  
E = margin of error =    4  
      
Thus,      
      
n =    76.34390625  
      
Rounding up,      
      
n =    77   [ANSWER]