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} } )](https://tex.z-dn.net/?f=%28x%5E%7B-%7D%20-%20t_%7B%5Cfrac%7B0.01%7D%7B2%7D%20%2C8%7D%20%5Cfrac%7BS.D%7D%7B%5Csqrt%7Bn%7D%20%7D%20%2Cx%5E%7B2%7D%20%20%2B%20t_%7B%5Cfrac%7B0.01%7D%7B2%7D%2C8%20%7D%20%5Cfrac%7BS.D%7D%7B%5Csqrt%7Bn%7D%20%7D%20%29)
![(570-3.354\frac{30}{\sqrt{9} } , 570+3.354\frac{30}{\sqrt{9} } )](https://tex.z-dn.net/?f=%28570-3.354%5Cfrac%7B30%7D%7B%5Csqrt%7B9%7D%20%7D%20%2C%20570%2B3.354%5Cfrac%7B30%7D%7B%5Csqrt%7B9%7D%20%7D%20%29)
(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>