Software design team would like to estimate the average time

Software design team would like to estimate the average time required for a new client to become proficient at working with one of their newly developed software products. Furthermore, they would like the resulting 90% confidence interval from this study to be no more than 10 minutes wide (TOTAL WIDTH). A pilot study done with a similar product yielded a mean of 135 minutes and a corresponding standard deviation of 20 minutes. Based on this information, how many subjects must be sampled in order for this team to meet their objective?

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 =    20  
E = margin of error = 10/2 =   5  
      
Thus,      
      
n =    43.28869527  
      
Rounding up,      
      
n =    44   [ANSWER]