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.

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

LASTNAME FIRSTNAME GENDER AGE CLASS BOARDED STATUS Bucknell Emma Female 59 First Cherbourg Survived Carter William Male 36 First Southampton Survived Crosby Edward Male 70 First Southampton Died Daniel Robert Male 27 First Southampton Survived Douglas Mary Female 27 First Cherbourg Survived Guggenheim Benjamin Male 46 First Cherbourg Died Harris Henry Male 45 First Southampton Died Pears Edith Female 22 First Southampton Survived Smith Lucien Male 24 First Cherbourg Died Stephenson Martha Female 52 First Cherbourg Survived Cameron Clear * 35 Second Southampton Survived Corbett Irene Female 30 Second Southampton Died Hocking Samuel Male 36 Second Southampton Died Knight Robert Male 39 Second Belfast Died Norman Robert Male 28 Second Southampton Died Padron-Manent Julian Male 26 * Cherbourg Survived Toomey Ellen Female 48 Second Southampton Survived Trout Jessie * 26 Second Southampton Survived West Constance Female 4 Second Southampton Survived Williams Charles Male 23 Second Southampton Survived Asplund Johan Male 23 Third Southampton Survived Bradley Bridget Female 22 Third Queenstown Survived Daly Margaret Female 30 Third Queenstown Survived Devaney Margaret Female 19 Third Queenstown Survived Dowdell Elizabeth Female 31 * Southampton Survived Jirjis Shaniini * 22 Third Cherbourg Survived Madsen Fridtjof Male 24 Third Southampton Survived Strandberg Ida Female 22 Third Southampton Died Torfa Assad Male 20 Third Cherbourg Died Touma Gerios Male 8 Third Cherbourg Survived

Explanation / Answer

Getting the standard deviation of the group using technology, we get

s = 14.08203

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 =    14.08203  
E = margin of error =    2  
      
Thus,      
      
n =    134.1297307  
      
Rounding up,      
      
n =    135 [ANSWER]

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