The statistic (n − 1)s² / σ² 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 σ². D)All of these choices are true.

Question

Quizplus · Accepted Answer

The given statistic is a ratio of the sample standard deviation to the population standard deviation, multiplied by a constant term. Therefore, it depends on the population variance (σ^2) and not on the sample size or the distribution of the sample. In addition, the numerator of the statistic follows a chi-squared distribution with n-1 degrees of freedom, which means that the denominator should be a constant multiple of σ^2 to result in a chi-squared distribution. Thus, the correct choice is C - the population is normally distributed with variance equal to σ^2.

The Statistic (N − 1)s2 / σ2 Has a Chi-Squared

The Statistic (N − 1)s² / σ² Has a Chi-Squared