From a list of all passengers onboard at the time of the collision, groups were

Question

From a list of all passengers onboard at the time of the collision, groups were formed with ten names in each group. Then three of these groups were were selected using simple random sampling without replacement. The thirty passengers from the three selected groups are in the table below. Cells with an * indicate that this information is not known.

D) How many randomly selected passengers would have to be selected to estimate the age of all passengers to within five years with 90% confidence?

9 AGE LASTNAME FIRSTNAME Bucknell 1 2 Crosby heim Beniamin Female Corbett 9 Norman Padron-Manent Julian 2 2 Constance Williams Queenstown Queenstown 3 Devaney

Explanation / Answer

Getting the standard deviation of the sample,

s = 14.08203

Note that      
      
n = z(alpha/2)^2 s^2 / E^2      
      
where      
      
alpha/2 =    0.05  
      
Using a table/technology,      
      
z(alpha/2) =    1.644853627  
      
Also,      
      
s = sample standard deviation =    14.08203  
E = margin of error =    2  
      
Thus,      
      
n =    134.1297307  
      
Rounding up,      
      
n =    135   [ANSWER]

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