Question

In 1912 the luxury liner Titanic on its first voyage across the Atlantic, struck an iceberg and sank. Some passengers got off the ship in lifeboats, but many died. Think of the Titanic disaster as an experiment in how the people of that time behaved when faced with death in a situation where only some can escape. The passengers are a sample from the population of their peers. Here is a table showing who survived the sinking of the Titanic based on whether they were crew members, or passengers booked in first-, second-, or third-class staterooms:

	crew	First	Second	Third	Total
Alive Dead	212 673	202 123	118 167	178 528	710 1491
Total	885	325	285	706	2201

. Calculate the survival rates (the number who survived divided by the number in the group) for each of the four groups. b. (1 mark) Write null and alternative hypotheses to assess whether group and survival are related. c. Is there strong evidence that the survival rates are not all the same? If not, what differences seem important?

Answer 1

a)

	crew	first	second	third
survival rate=	24.0%	62.2%	41.4%	25.2%

b)

Ho: group and survival are related

H1: group and survival are not related

c)

Chi-Square Test of independence
	Observed Frequencies
	crew	first	second	third			Total
alive	212	202	118	178			710
dead	673	123	167	528			1491
Total	885	325	285	706			2201
	Expected frequency of a cell = sum of row*sum of column / total sum
	Expected Frequencies
	crew	first	second	third			Total
alive	885*710/2201=285.484	325*710/2201=104.839	285*710/2201=91.935	706*710/2201=227.742			710
dead	885*1491/2201=599.516	325*1491/2201=220.161	285*1491/2201=193.065	706*1491/2201=478.258			1491
Total	885	325	285	706			2201
	(fo-fe)^2/fe
alive	18.9148	90.0461	7.390	10.864
dead	9.0071	42.8791	3.519	5.173

Chi-Square Test Statistic,χ² = Σ(fo-fe)^2/fe =   187.7932  
      
Level of Significance =   0.05  
Number of Rows =   2  
Number of Columns =   4  
Degrees of Freedom=(#row - 1)(#column -1) = (2- 1 ) * ( 4- 1 ) =   3  
      
p-Value =   0.0000 [Excel function: =CHISQ.DIST.RT(χ²,df) ]
Decision:    p-value < α , Reject Ho

There is strong evidence that the survival rates are not all the same

in group first class, survival rate is highest