Question

Before any order is shipped, inspectors at Alvarez Manufacturing test a sample of finished units for breaking strength. You select a simple random sample of 16 units from a recently completed order and find that the sample average breaking strength is 799 pounds. Because you do not know the population standard deviation, you calculate a sample standard deviation of the breaking strengths of 29 pounds. Assume that the population is normally distributed. Construct a 99% confidence interval estimate of the average breaking strength you could expect to find if all the units in the order were tested.

Answer 1

x̅ = 799, s = 29, n = 16

99% Confidence interval :

At α = 0.01 and df = n-1 = 15, two tailed critical value, t-crit = T.INV.2T(0.01, 15) = 2.947

Lower Bound = x̅ - t-crit*s/√n = 799 - 2.947 * 29/√16 = 777.636

Upper Bound = x̅ + t-crit*s/√n = 799 + 2.947 * 29/√16 = 820.364

777.636 < µ < 820.364