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

Identify the null and alternative hypotheses corresponding to the stated claim.

Short answer

The null hypothesis for this test is as follows:

The survival of the passenger is independent of whether he/she is a man, woman, boy or girl.

The alternative hypothesis for this test is as follows:

The survival of the passenger is not independent of whether he/she is a man, woman, boy or girl.

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.

Hypotheses

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

The null hypothesis and the alternative hypothesis is as follows:

\({H_0}:\)The survival of the passenger is independent of whether he/she is a man, woman, boy or girl.

\({H_1}:\)The survival of the passenger is not independent of whether he/she is a man, woman, boy or girl.