The highway safety department conducted a study of the drivi

The highway safety department conducted a study of the driving habits of individuals. they computed a %95 confidence interval estimate for the speed of all cars to be (58.04, 61.96). what sample size was used if the population standard deviation was reported to be 11 mph?

Solution

Note that      
      
n = z(alpha/2)^2 s^2 / E^2      
      
where      
      
alpha/2 = (1 - confidence level)/2 =    0.025  
      
Using a table/technology,      
      
z(alpha/2) =    1.959963985  
      
Also,      
      
s = sample standard deviation =    11  
E = margin of error = (upper- lower)/2 = (61.96-58.04)/2 =   1.96  
      
Thus,      
      
n =    120.9955532  
      
Rounding up,      
      
n =    121   [ANSWER]