# PS4.docx - CSSS/SOC/STAT 221 Summer 2021 Name: Neil Dadlani...

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CSSS/SOC/STAT 221 Summer 2021 Name: Neil Dadlani Collaborators: __________________________________________ Student number: 2036577 Problem Set 4: Using a chi-square test to identify differences in survival rates between different populations Early on the morning of 15 April 1912, the ocean linerRMSTitanicsank in the North Atlantic, on the ship’s first voyage. Tragically, approximately 68% of the ship’s passengers and crew perished. The table below describes the frequencies of those who survived the catastrophe and those who perished, separated according to passenger class (1st, 2nd, and 3rdclass, plus crew). Observed counts ( O i, j )PerishedSurvivedRow totals 1stclass122203325 2ndclass167118285 3rdclass528178706 Crew673212885 Column totals14907112201 The overall survival proportion was approximately 32% (ppooled =711/2201 ), but some groups fared better than others: 62% of the 1st-class passengers and 41% of the 2nd -class passengers survived, in contrast to 25% of the 3rd-class passengers and 24% of the ship’s crew. Given this pattern in the sample, it is reasonable to wonder if different groups had unequal access to the means of survival. Conversely, we might wonder if every group was exposed to the same probability of survival, in which case the pattern of variability we see in the sample would be the result of random sampling error alone. We can treat the probability of survivalπas the focus of a null hypothesis. If survival is independent of passenger class, then we can set our null value top pooled and stat our hypothesis as— H0:π1st=π2nd=π3rd=πcrew=p pooled —which we can test with a chi-square test for independence.

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