24. Suppose we want to estimate the average age of Titanic passengers. We want t

Question

24. Suppose we want to estimate the average age of Titanic passengers. We want to stratify by (adult) males, (adult) females, and children but we don't know the population sizes of these groups on the ship. We use double sampling as a strategy. In Phase 1, we randomly sample 260 passengers and research if each is male, female, or a child. Here are the results: Tally Phase1Sample Count male 146 80 34 female child a. Based on the sample above, what percentage of passengers are (adult) males, what percentage are (adult) females, and what percentage are children? It takes time to investigate the age of each passenger, so we take a smaller random sample of 65 passengers and research the average age for each. Using the following results from Phase 2, estimate the mean age with a bound on the error of estimation. (Note: SE Mean =s//n) b. Statistics Grou ChildrensAges 99.65 FemaleAges 033.80 MaleAges N Mean SE Mean 1.96 2.88 1.98 36 30.14 The actual average age of all passengers on board the Titanic is 29.4 years old. Based on your answer to part b, does this value seem likely? c.

Explanation / Answer

a)

Male: - 146/260*100=56.15%

Female: - 80/260*100=30.77%

Children: - 34/260*100=13.08%

b)

Average=(9*9.65)+(20*33.80)+(36*30.14)/65

=28.43

c)

Yes because it is closer to answer computed in b and the average value might go up based on the sample size (or the entire population).

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