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 590⁢HP. 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 that,

Point estimate = sample mean = = 580

sample standard deviation = s = 45

sample size = n = 25

Degrees of freedom = df = n - 1 = 25 - 1 = 24

At 99% confidence level

= 1 - 99%

=1 - 0.99 =0.01

/2 = 0.005

t/2,df = t_0.005,24 = 2.797

Margin of error = E = t_/2,df * (s /n)

= 2.797 * ( 45/ 25)

Margin of error = E = 25.17

The 99% confidence interval estimate of the population mean is,

- E < < + E

580 - 25.17 < < 580 + 25.17

( 554.83 HP < < 605.17 HP )