Chapter 15, Problem 1CR

a.

To determine

Find the hypotheses in a chi-square test for independence.

Explanation of Solution

The test hypotheses are given below:

Null hypothesis:

$H_0:$ Variable A and B are independent.

Alternative hypothesis:

$H_1:$ Variable A and B are not independent.

b.

To determine

Explain why it is known as test of frequencies.

Explanation of Solution

The chi-square test for independence is a test based on frequencies. Thus, it is known as test of frequencies.

c.

To determine

Find the distribution that is used in this test.

Explanation of Solution

In chi-square test for independence, the shape of the population from which the sample has taken is not specified. Therefore it called distribution free test.

d.

To determine

Find the degrees of freedom for a $r\times c$ contingency table.

Explanation of Solution

The degrees of freedom for a $r\times c$ contingency table is,

$\text{d}\text{.f}=\left(r-1\right)\left(c-1\right)$, where r is the number of row of the contingency table and c is the number of column of the contingency table.