Which of the following statements are correct about Chi-Square test?

Sourav PanSeptember 10, 2024

Answered

Here’s an analysis of each statement regarding the Chi-Square test:

(A) The only parameter of a Chi-Square distribution is its number of degrees of freedom.

• Correct. The Chi-Square distribution is defined by its degrees of freedom (df). Unlike other distributions, the Chi-Square distribution does not have parameters such as mean or standard deviation. The degrees of freedom determine the shape of the distribution.

(B) The null hypothesis in a Chi-Square test is rejected when the calculated value of the variable exceeds its critical value.

• Correct. In a Chi-Square test, the null hypothesis is rejected if the calculated Chi-Square statistic exceeds the critical value from the Chi-Square distribution table at a given significance level. This indicates that the observed data significantly deviates from what was expected under the null hypothesis.

(C) The rejection region in a goodness of fit test lies only in the right tail of the distribution.

• Correct. For a Chi-Square test for goodness of fit, the rejection region is located in the right tail of the Chi-Square distribution. This is because the Chi-Square statistic is always positive and any large value suggests a significant deviation from the expected distribution.

(D) The Chi-Square test is a parametric test.

• Incorrect. The Chi-Square test is not considered a parametric test. It is a non-parametric test because it does not assume a specific distribution for the population data; rather, it assesses the goodness of fit or independence based on categorical data.

(E) At α = 0.05 and V = 1, the critical value of χ2\chi^2χ2 is equal to the Z-value at the same level of significance.

• Incorrect. The critical value of χ2\chi^2χ2 at $\alpha =0.05$ and $V=1$ (degrees of freedom) is not equal to the Z-value at the same significance level. The Z-value for $\alpha =0.05$ (one-tailed) is approximately 1.645, while the Chi-Square critical value for $\alpha =0.05$ with 1 degree of freedom is approximately 3.841. The Chi-Square and Z-distributions are different and are used in different types of statistical tests.

In summary, the correct statements are:

• (A) The only parameter of a Chi-Square distribution is its number of degrees of freedom.
• (B) The null hypothesis in a Chi-Square test is rejected when the calculated value of the variable exceeds its critical value.
• (C) The rejection region in a goodness of fit test lies only in the right tail of the distribution.