Question

Which of the following statements is correct?

• A. The value of Chi-square can be positive as well as negative
• B. Chi-square test is used for testing equality of several proportions
• C. In a 4x3 contingency table, the degrees of freedom for chi-square is 8
• D. Chi-square test is used for testing equality of two population variances

Hint:

Exam Tip:
Chi-square test applications:

• Goodness of fit.
• Test of independence.
• Test of homogeneity (testing equality of proportions). Degrees of freedom:

• Goodness of fit: \((k - 1)\).
• Contingency table: \((r - 1)(c - 1)\).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The chi-square (\(\chi^2\)) test is a non-parametric test used for various purposes. We need to identify the correct statement.

Step 2: Analyzing Each Option:

• (A) The value of Chi-square can be positive as well as negative:
This is false. The chi-square statistic is always non-negative (zero or positive).
It is a sum of squared differences, so it cannot be negative.
• (B) Chi-square test is used for testing equality of several proportions:
This is true. The chi-square test of homogeneity or independence is used to test if several populations have the same proportions.
• (C) In a 4x3 contingency table, the degrees of freedom for chi-square is 8:
For a contingency table with \(r\) rows and \(c\) columns, the degrees of freedom are \((r - 1)(c - 1)\).
For \(4 \times 3\), df = \((4 - 1)(3 - 1) = 3 \times 2 = 6\), not 8.
So, this statement is false.
• (D) Chi-square test is used for testing equality of two population variances:
This is false. The F-test is used for testing equality of two population variances.
The chi-square test is used for testing a single variance or for goodness of fit.

Step 3: Final Answer:
Therefore, option (B) is correct.