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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

Two-way tables
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asked 2021-01-30
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.
\(\begin{array}{l|c|c|c|c} & \text { First } & \text { Second } & \text { Third } & \text { Total } \\ \hline \text { Survived } & 197 & 94 & 151 & 442 \\ \hline \text { Died } & 122 & 167 & 476 & 765 \\ \hline \text { Total } & 319 & 261 & 627 & 1207 \\ \end{array}\)

Expert Answers (1)

2021-01-31
Given: \(\begin{array}{l|c|c|c|c} & \text { First } & \text { Second } & \text { Third } & \text { Total } \\ \hline \text { Survived } & 197 & 94 & 151 & 442 \\ \hline \text { Died } & 122 & 167 & 476 & 765 \\ \hline \text { Total } & 319 & 261 & 627 & 1207 \\ \end{array}\)
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.
\(E_{11}=\frac{r_1 \times c_1}{n}=\frac{442 \times 319}{1207} \approx 116.82\)
\(E_{12}=\frac{r_1 \times c_2}{n}=\frac{442 \times 261}{1207} \approx 95.58\)
\(E_{13}=\frac{r_1 \times c_3}{n}=\frac{442 \times 627}{1207} \approx 229.61\)
\(E_{21}=\frac{r_2 \times c_1}{n}=\frac{765 \times 319}{1207} \approx 202.18\)
\(E_{22}=\frac{r_2 \times c_2}{n}=\frac{765 \times 261}{1207} \approx 165.42\)
\(E_{23}=\frac{r_2 \times c_3}{n}=\frac{765 \times 627}{1207} \approx 397.39\) 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.
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In 1912 the Titanic struck an iceberg and sank on its first voyage. Some passengers got off the ship in lifeboats, but many died. The following two-way table gives information about adult passengers who survived and who died, by class of travel.
\(\begin{array} {lc} & \text{Class} \\ \text {Survived} & \begin{array}{c|c|c|c} & \text { First } & \text { Second } & \text { Third } \\ \hline \text { Yes } & 197 & 94 & 151 \\ \hline \text { No } & 122 & 167 & 476 \\ \end{array}\\ \end{array}\)
Suppose we randomly select one of the adult passengers who rode on the Titanic. Define event D as getting a person who died and event F as getting a passenger in first class. Find P (not a passenger in first class and survived).

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