The statistic ( n - 1)s ² \ s ² has a chi-squared distribution with n - 1 degrees of freedom if: A)the sample has a Student t -distribution with degrees of freedom equal to n - 1. B)the sample is normally distributed with variance equal to s ². C)the population is normally distributed with variance equal to s ². D)All of these choices are true.

Question

Quizplus · Accepted Answer

The statistic $(n - 1)s^2 / \sigma^2$ follows a chi-squared distribution with $n - 1$ degrees of freedom if the population from which the sample is drawn is normally distributed with variance equal to $\sigma^2$. This is a fundamental result in statistics related to the properties of the sample variance in a normally distributed population. Choices A and B do not directly relate to the conditions under which the given statistic follows a chi-squared distribution.

The Statistic ( N - 1)s 2 \ S 2

The Statistic ( N - 1)s ² \ S ²