Question

Questions 6–10 refer to the sample data in the following table, which describes the fate of the passengers and crew aboard the Titanic when it sank on April 15, 1912. Assume that the data are a sample from a large population and we want to use a 0.05 significance level to test the claim that surviving is independent of whether the person is a man, woman, boy, or girl.

	Men	Women	Boys	Girls
Survived	332	318	29	27
Died	1360	104	35	18

What distribution is used to test the stated claim (normal, t, F, chi-square, uniform)?

Short answer

The chi-square distribution is used to test the given claim.

Step-by-step solution

Given information

A contingency table is constructed that shows the number of passengers who survived/died according to whether they were male, female, boy or girl.

Distribution of the test statistic

It is required to test the claim that the survival of the passenger is independent of whether the person is a man, woman, boy or girl.

Thus, it is a test of the independence of attributes that involves nominal variables or variables that consist of categories.

Here, the row variable consists of labels “survived” and “died” and the column variable consists of labels “men”, “women”, “boys” and “girls”.

Such types of tests that involve categorical variables are carried out using the chi-square distribution.

Moreover, the other hypotheses tests involving normal distribution, t-distribution and F-distribution are applied only when the variables are quantitative and not qualitative.

Uniform distribution is not used to conduct hypothesis tests.

Therefore, the distribution of the test statistic to test the given claim is the chi-square distribution.