A study plans to investigate the average time a 16 year old

A study plans to investigate the average time a 16 year old spends playing video games each week. From studies of similar age groups it is believed the standard deviation should be near 8.1 hours. The study wants a 90% confidence interval to have a margin of error of 0.5 (the nearest half hour).   How many 16 year olds are they going to need to sample?

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 =    8.1  
E = margin of error =    0.5  
      
Thus,      
      
n =    710.0428241  
      
Rounding up,      
      
n =    711   [ANSWER]