A sample of n observations is taken from a population. When performing statistical inference about a population variance, the appropriate chi-square distribution has

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When performing statistical inference about a population variance, the appropriate chi-square distribution has n - 1 degrees of freedom. This is because estimating the population variance involves using the sample mean, which represents one degree of freedom already. The remaining n-1 observations contribute to the estimate of the variance, hence n-1 degrees of freedom.

A Sample of N Observations Is Taken from a Population