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

Is the hypothesis test left-tailed, right-tailed, or two-tailed?

Short answer

The given hypothesis test is right-tailed.

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.

Tail of the test

It is known that the tests of independence with a contingency table are always right-tailed.

In the test of independence of attributes, the chi-square test statistic is as follows:

\({\chi ^2} = \sum {\frac{{{{\left( {O - E} \right)}^2}}}{E}} \)

Suppose the discrepancy between the observed and expected frequencies is considerable. In that case, the test statistic value will shift to the right side of the curve, indicating the rejection of the null hypothesis (if it exceeds a certain value). Also, a large deviation means that the observed frequencies do not match the expected frequencies and the two attributes are not independent.

Furthermore, if the difference between the observed and the expected frequencies is less, the test statistic value will shift to the left side of the curve, implying that the given frequencies match the expected frequencies. As a result, the two attributes will be independent.

The claim to be tested is that the passenger’s survival is independent of whether the person is a man, woman, boy or a girl.

This implies that it is the independence of attributes test.

Therefore, the given hypothesis test is said to be a right-tailed test.