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 590HP. Twenty five engines are randomly selected for horsepower testing. The sample has an average maximum HP of 580 with a standard deviation of 45⁢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=0.01. Round your answers to two decimal places.

Answer 1

Solution:

Given:

Sample Size = n = 25

Sample Mean =

Sample Standard Deviation = s = 45

We have to calculate a confidence interval for the average maximum HP for the experimental engine.

Significance level =  α=0.01.

Thus c = confidence level = 1 -  α=1 - 0.01 = 0.99

Formula:

where

tc is t critical value for c = 99%  confidence level

Thus two tail area = 1 - c = 1 - 0.99 = 0.01

df = n - 1 =  25 - 1 =24
Look in  t table for df = 24 and two tail area = 0.01 and find t critical value

t_c = 2.797

Thus

Thus

Thus 99% confidence interval  for the average maximum HP for the experimental engine is between 554.83 HP and 605.17 HP.