The standard IQ test has a mean of 96 and a standard deviati

The standard IQ test has a mean of 96 and a standard deviation of 14. We want to be 99% certain that we are within 4 IQ points of the true mean. Determine the required sample size.

A. 178

B. 10

C. 1

D. 82

Solution

Note that      
      
n = z(alpha/2)^2 s^2 / E^2      
      
where      
      
alpha/2 = (1 - confidence level)/2 =    0.005  
      
Using a table/technology,      
      
z(alpha/2) =    2.575829304  
      
Also,      
      
s = sample standard deviation =    14  
E = margin of error =    4  
      
Thus,      
      
n =    81.27748336  
      
Rounding up,      
      
n =    82   [OPTION D]