 # In 1912 the luxury liner Titanic struck an iceberg and sank. Some passengers got off the ship in lifeboats, but many died. The two-way table gives inf Kye 2021-01-30 Answered
In 1912 the luxury liner Titanic struck an iceberg and sank. Some passengers got off the ship in lifeboats, but many died. The two-way table gives information about adult passengers who survived and who died, by class of travel. Check the conditions for performing a chisquare test for association.
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Given:
The null hypothesis states that there is no difference in the distribution of the categorical variable for exch of the populations/treatments. The alternative hypothesis states that there is a difference.
${H}_{0}$: The distribution of candy chosen is the same for each survey type.
${H}_{a}$: The distribution of candy chosen is not the same for each survey type.
The expected frequencies are the product of the column and row total,divided by the table total.
${E}_{11}=\frac{{r}_{1}×{c}_{1}}{n}=\frac{442×319}{1207}\approx 116.82$
${E}_{12}=\frac{{r}_{1}×{c}_{2}}{n}=\frac{442×261}{1207}\approx 95.58$
${E}_{13}=\frac{{r}_{1}×{c}_{3}}{n}=\frac{442×627}{1207}\approx 229.61$
${E}_{21}=\frac{{r}_{2}×{c}_{1}}{n}=\frac{765×319}{1207}\approx 202.18$
${E}_{22}=\frac{{r}_{2}×{c}_{2}}{n}=\frac{765×261}{1207}\approx 165.42$
${E}_{23}=\frac{{r}_{2}×{c}_{3}}{n}=\frac{765×627}{1207}\approx 397.39$ Conditions
The conditions for performing a chi-square test of homogeneity /independence are: Random, Independent: (10%), Large counts.
Random: Not satisfied, because the passengers of the titanic were not randomly selected..
Independent: Satisfied, because the 1207 people are less than 10% of all people (since there are more than 12070 people).
Large counts: Satisfied, because all expected counts are at least 5.
Since the random condition is not satisfied, it is not appropriate to carry out a test of homogeneity ‘independence.
All conditions are satisfied.