From a list of all passengers onboard at the time of the col

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

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]

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 select

From a list of all passengers onboard at the time of the col

Solution

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