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 530HP . Sixteen engines are randomly selected for horsepower testing. The sample has an average maximum HP of 500 with a standard deviation of 50HP . 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=0.1 . Round your answers to two decimal places.

Answer 1

Solution

Back-up Theory

Let X = maximum HP of the experimental engine

Given X ~ N(μ, σ²),

L100(1 - α) % Confidence Interval for population mean μ, when σ is not known is: Xbar ± MoE... (1)

where

MoE = (t_{n- 1, α /2})s/√n ....................................................................................................................... (2)

with

Xbar = sample mean,

t_{n – 1, α /2} = upper (α/2)% point of t-distribution with (n - 1) degrees of freedom,

s = sample standard deviation and

n = sample size.

Now to work out the solution,

Vide (2), MoE = 21.913 and

Vide (1), 90% confidence interval for the average maximum HP for the experimental engine is:

[478.09, 521.91] Answer

Details of calculations

Given	α	0.1	1 - (α/2) =	0.95
	n	16	SQRT(n)	4
	Xbar	500	n - 1	15
	s	50
tα/2		1.7531
90% CI for μ		500	±	21.9131
Lower Bound		478.0869
Upper Bound		521.9131

DONE