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sesenic [268]
3 years ago
15

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 540HP . Nine engines are randomly selected for horsepower testing. The sample has an average maximum HP of 570 with a standard deviation of 30HP. 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.
Mathematics
1 answer:
Maurinko [17]3 years ago
4 0

Answer:

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

(536.46, 603.54)

Step-by-step explanation:

<u><em>Step:-1</em></u>

Given that the mean of the Population = 540HP

Given that the size of the sample  'n' = 9

Given that the mean of the sample = 570HP

Given that the sample standard deviation = 30HP

<u><em>Step(ii):-</em></u>

<u><em>Degrees of freedom = n-1 =9-1 =8</em></u>

<u><em>t₀.₀₀₅ = 3.3554</em></u>

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

(x^{-} - t_{\frac{0.01}{2} ,8} \frac{S.D}{\sqrt{n} } ,x^{2}  + t_{\frac{0.01}{2},8 } \frac{S.D}{\sqrt{n} } )

(570-3.354\frac{30}{\sqrt{9} } , 570+3.354\frac{30}{\sqrt{9} } )

(570 - 33.54 , 570+33.54)

(536.46 , 603.54)

<u><em>Final answer</em></u> :-

<em>The 99% of a confidence interval for the average maximum HP for the experimental engine.</em>

<em>(536.46, 603.54)</em>

<em></em>

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