Expert Answer to "In 1912 the luxury liner Titanic struck an..."

Kye

Answered question

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

Answer & Explanation

krolaniaN

Skilled2021-01-31Added 86 answers

Given:

\begin{array}{lcccc} First & Second & Third & Total \\ Survived & 197 & 94 & 151 & 442 \\ Died & 122 & 167 & 476 & 765 \\ 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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