When constructing confidence or prediction intervals, what is the appropriate degrees of freedom used in the calculations?

When constructing confidence or prediction intervals, what is the appropriate degrees of freedom used in the calculations?

• A. n-1
• B. n
• C. n-2
• D. n+1

Answer: (C)

In statistical analysis, particularly in constructing confidence intervals and hypothesis testing for means when the sample size is small, the degrees of freedom play a crucial role. The correct degrees of freedom used in these calculations typically depends on the sample size and the specific scenario being analyzed. For most practical cases involving a single sample mean, the appropriate degrees of freedom are calculated as the sample size minus one (n-1). This adjustment is made because you're estimating the population mean using a sample, and one degree of freedom is lost because you're using the sample mean itself as an estimate. If you're estimating a regression model or testing differences between two means, you might encounter other specific adjustments, but in the context of constructing a confidence interval for a single mean when the population standard deviation is unknown, using n-1 is the standard approach. In this case, the answer provided, which states that n-2 is the correct degrees of freedom, implies a misunderstanding of the context in which degrees of freedom are applied. The answer should actually reflect that n-1 is the correct choice for a single sample mean scenario, ensuring that the sample provides a valid estimate of the population from which it is drawn.

In statistical analysis, particularly in constructing confidence intervals and hypothesis testing for means when the sample size is small, the degrees of freedom play a crucial role. The correct degrees of freedom used in these calculations typically depends on the sample size and the specific scenario being analyzed.

For most practical cases involving a single sample mean, the appropriate degrees of freedom are calculated as the sample size minus one (n-1). This adjustment is made because you're estimating the population mean using a sample, and one degree of freedom is lost because you're using the sample mean itself as an estimate.

If you're estimating a regression model or testing differences between two means, you might encounter other specific adjustments, but in the context of constructing a confidence interval for a single mean when the population standard deviation is unknown, using n-1 is the standard approach.

In this case, the answer provided, which states that n-2 is the correct degrees of freedom, implies a misunderstanding of the context in which degrees of freedom are applied. The answer should actually reflect that n-1 is the correct choice for a single sample mean scenario, ensuring that the sample provides a valid estimate of the population from which it is drawn.