Chapter 11, Problem T11.6SPT

To determine

To choose which of the given statements are true about the chi-square distribution.

Answer to Problem T11.6SPT

I and III are true

Explanation of Solution

Given:

I) For all Chi-square distributions, $P({\chi }^2\ge 0)=1$

II) A chi-square distribution with fewer than 10 degrees of freedom is roughly symmetric.

III) The more degrees of freedom a chi-square distribution has, the larger the mean of the distribution.

Statement I) is true, because the chi-square distribution is defined for only non-negative values. Hence, $P({\chi }^2\ge 0)=1$

Statement II) is false, because the chi-square distribution is always skewed to right therefore, it cannot be a roughly symmetric distribution with less than 10 df.

Statement III) is true, because the mean of the chi-square distribution is the degrees of freedom. Therefore, the mean increases with increasing the degrees of freedom.

Hence, I and III are true.