In developing a confidence interval for the population standard deviation ,we make use of the fact that the sampling distribution of the sample standard deviation s is not the normal distribution or the t-distribution,but rather a right-skewed distribution called the chi-square distribution,which (for this procedure)has n - 1 degrees of freedom.

Question

In developing a confidence interval for the population standard deviation  ,we make use of the fact that the sampling distribution of the sample standard deviation s is not the normal distribution or the t-distribution,but rather a right-skewed distribution called the chi-square distribution,which (for this procedure)has n - 1 degrees of freedom.

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This statement is true. When constructing a confidence interval for the population standard deviation, we use the chi-square distribution with n-1 degrees of freedom as the sampling distribution of the sample standard deviation. This is because the sample standard deviation is calculated using squared deviations, and these deviations follow a chi-square distribution. This distribution is right-skewed and not normal or t-distributed.

In Developing a Confidence Interval for the Population Standard Deviation