In 1912 the luxury liner Titanic on its first voyage across the Atlantic, struck an iceberg...

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In 1912 the luxury liner Titanic on its first voyage across theAtlantic, struck an iceberg and sank. Some passengers got off theship in lifeboats, but many died. Think of the Titanic disaster asan experiment in how the people of that time behaved when facedwith death in a situation where only some can escape. Thepassengers are a sample from the population of their peers. Here isa table showing who survived the sinking of the Titanic based onwhether 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 whosurvived divided by the number in the group) for each of the fourgroups. b. (1 mark) Write null and alternative hypotheses to assesswhether group and survival are related. c. Is therestrong evidence that the survival rates are not all the same? Ifnot, what differences seem important?

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4.3 Ratings (566 Votes)

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

Ho: group and survival are related

H1: group and survival are not related

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,Ï‡Â² = Î£(fo-fe)^2/fe =Â Â 187.7932Â Â
Â Â Â Â Â
Level of Significance =Â Â 0.05Â Â
Number of Rows =Â Â 2Â Â
Number of Columns =Â Â 4Â Â
Degrees of Freedom=(#row - 1)(#column -1) = (2- 1 ) * ( 4- 1 ) =Â Â 3Â Â
Â Â Â Â Â
p-Value =Â Â 0.0000 [Excel function: =CHISQ.DIST.RT(Ï‡Â²,df) ]
Decision: Â Â p-value < Î± , Reject Ho

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

in group first class, survival rate is highest

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