Question

High-power experimental engines are being developed by the Stevens Motor Company for use in its new sports coupe. The engineers have calculated the maximum horsepower for the engine to be 700⁢HP. Nine engines are randomly selected for horsepower testing. The sample has an average maximum HP of 730 with a standard deviation of 70⁢HP. Assume the population is normally distributed.

Calculate a confidence interval for the average maximum HP for the experimental engine. Use a significance level of α=0.05. Round your answers to two decimal places.

Answer 1

sample mean, xbar = 730
sample standard deviation, s = 70
sample size, n = 9
degrees of freedom, df = n - 1 = 8

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, tc = t(α/2, df) = 2.306

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (730 - 2.306 * 70/sqrt(9) , 730 + 2.306 * 70/sqrt(9))
CI = (676.19 , 783.81)