Question 1205266
sample size is 16.
sample mean is 67.5
sample standard deviation is 1.1


since you're dealing with a sample standard deviation rather than the population standard deviation, use the t-score rather than the z-score.


critical t-score for 99% confidence interval with 15 degrees of freedom is equal to plus or minus t = 2.9467.


standard error = standard deviation / square root of sample size = 1.1 / sqrt(16) = .275.


low end of the confidence interval critical t-score formula is -2.9467 = (x - 67.5) / .275.
solve for x to get x = -2.9467 * .275 + 67.5 = 66.68966.


high end of the confidence interval critical t-score formula is 2.9467 = (x - 67.5) / .275
solve for x to get x = 2.9467 * .275 + 67.5 = 68.31034.


your 99% confidence interval is from 66.68966 to 68.31034.


here's what 99% confidence interval of the t-score like on a graph.


<img src = "http://theo.x10hosting.com/2023/120901.jpg">