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.

$\begin{array}{lcccc}& \text{First}& \text{Second}& \text{Third}& \text{Total}\\ \text{Survived}& 197& 94& 151& 442\\ \text{Died}& 122& 167& 476& 765\\ \text{Total}& 319& 261& 627& 1207\end{array}$

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krolaniaN

Answered 2021-01-31
Author has **86** answers

Given: $\begin{array}{lcccc}& \text{First}& \text{Second}& \text{Third}& \text{Total}\\ \text{Survived}& 197& 94& 151& 442\\ \text{Died}& 122& 167& 476& 765\\ \text{Total}& 319& 261& 627& 1207\end{array}$

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.

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.

The expected frequencies are the product of the column and row total,divided by the table total.

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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