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 790HP790⁢HP. Nine engines are randomly selected for horsepower testing. The sample has an average maximum HP of 900900 with a standard deviation of 85HP85⁢HP. Assume the population is normally distributed.

Step 1 of 2 :  

Calculate a confidence interval for the average maximum HP for the experimental engine. Use a significance level of α=0.01α=0.01. Round your answers to two decimal places.

Step 2:

does this fail the null hypothesis or not and why

Answer 1

1)

sample mean, xbar = 900
sample standard deviation, s = 85
sample size, n = 9
degrees of freedom, df = n - 1 = 8

Given CI level is 99%, hence α = 1 - 0.99 = 0.01
α/2 = 0.01/2 = 0.005, tc = t(α/2, df) = 3.355

ME = tc * s/sqrt(n)
ME = 3.355 * 85/sqrt(9)
ME = 95.058

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (900 - 3.355 * 85/sqrt(9) , 900 + 3.355 * 85/sqrt(9))
CI = (804.94 , 995.06)

2)

not fail the null hypothesis becuase confidenc einterval does not contain 790