For a 99% confidence interval estimation based on a sample of size 10, what is the t value?

To determine the correct t value for a 99% confidence interval with a sample size of 10, it is essential to consider the degrees of freedom, which are calculated as the sample size minus one. In this case, with a sample size of 10, there would be 9 degrees of freedom (10 - 1 = 9).

The t distribution is used here because the sample size is relatively small (less than 30), and it provides a more accurate representation of the variability in the sample compared to the normal distribution. For a 99% confidence level, you are looking for the t value that captures the central 99% of the distribution with the specified degrees of freedom.

By searching in a t distribution table or using a t-distribution calculator for 9 degrees of freedom and a 99% confidence interval, the t value that corresponds to the upper tail of 0.005 (since 1% significance level split across two tails results in 0.005 for one tail) is typically found to be 3.250.

This t value is critical in calculating the margin of error for the confidence interval, allowing you to establish a range in which the true population parameter is likely to fall with the specified level