SOLUTION: Assume that the heights of bookcases are normally distributed. A random sample of 16 bookcases in one company have a mean height of 67.5 inches and a standard deviation of 1.1 inch

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Question 1205266: Assume that the heights of bookcases are normally distributed. A random sample of 16 bookcases in one company have a mean height of 67.5 inches and a standard deviation of 1.1 inches. Construct a​ 99% confidence interval for the population standard​ deviation. Round to three decimal places.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
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.