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Chapter 1: Q9CQQ (page 1)

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

Find the number of degrees of freedom.

Short Answer

Expert verified

The number of degrees of freedom is equal to 3.

Step by step solution

01

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.

02

Degrees of freedom

The test statistic under the test for independence of attributes follows a chi-square distribution with the following degrees of freedom:

\(df = \left( {r - 1} \right)\left( {c - 1} \right)\)

where

r denotes the number of rows

c denotes the number of columns

Here, r is equal to 2 and c is equal to 4.

Thus, the number of degrees of freedom is equal to:

\(\begin{array}{c}df = \left( {r - 1} \right)\left( {c - 1} \right)\\ = \left( {2 - 1} \right)\left( {4 - 1} \right)\\ = 3\end{array}\)

Therefore, the number of degrees of freedom is equal to 3.

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Subject


12345
White8.75.97.36.25.9
Red4.915.594.444.85.17

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