Question

As the number of degrees of freedom increases, the graph of the chi-square distribution looks more and more symmetrical.

A. True
B. False

Answer 1

The graph of the chi-square distribution becomes less symmetrical as the number of degrees of freedom increases.

Step-by-step explanation:

The statement is False. As the number of degrees of freedom increases, the graph of the chi-square distribution becomes less symmetrical and more skewed to the right.

The shape of the chi-square distribution depends on the degrees of freedom (df). For df > 90, the distribution approximates the normal distribution, but for smaller degrees of freedom, it is more skewed.

For example, let's consider two chi-square distributions: one with 5 degrees of freedom and another with 20 degrees of freedom. The distribution with 5 degrees of freedom will be more right-skewed and less symmetrical compared to the distribution with 20 degrees of freedom.