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 830HP. Twenty five engines are randomly selected for horsepower testing. The sample has an average maximum HP of 880 with a standard deviation of 55HP. 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=0.01. Round your answers to two decimal places.

Answer 1

The 99% of a confidence interval for the average maximum HP for the experimental engine. (843.0906, 916.9094)

Given,

In the question:

Given that the mean of the Population = 830HP

Given that the size of the sample  'n' = 25

Given that the mean of the sample = 880HP

Given that the sample standard deviation = 55HP

To find the confidence interval for the average maximum HP for the experimental engine.

Use a significance level of α=0.01.

Now, According to the question:

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

t₀.₀₀₅ = 3.3554

The 99% of a confidence interval for the average maximum HP for the experimental engine.

$(x -\frac{t_0_._0_0_1}{2},24\frac{S.D.}{\sqrt{n} } , x^2 +\frac{t_0_._0_0_1}{2},24\frac{S.D.}{\sqrt{n} })$

(880 - 3.3554 $\frac{55}{\sqrt{25} }$ , 880 + 3.3554 $\frac{55}{\sqrt{25} }$)

(843.0906, 916.9094)

Hence, The 99% of a confidence interval for the average maximum HP for the experimental engine. (843.0906, 916.9094)

Learn more about Significance level at:

brainly.com/question/13909985

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