The statistic (n - 1)s² / $\sigma$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 s². C) the population is normally distributed with variance equal to $\sigma$². D) All of these choices are true.

Question

Quizplus · Accepted Answer

The given statistic follows a chi-squared distribution with degrees of freedom equal to n-1 if the population is normally distributed with variance equal to s^2. Therefore, the correct choice is C, which states that the population is normally distributed with variance equal to σ^2. The other choices are incorrect as they do not fulfill the necessary conditions for a chi-squared distribution.

The Statistic (N - 1)s2 σ\sigmaσ 2 Has a Chi-Squared Distribution with N - 1 Degrees

The Statistic (N - 1)s² $\sigma$ ² Has a Chi-Squared Distribution with N - 1 Degrees