Answer:
The 95 % confidence interval of the population mean for the weights of adult elephants
(11,629.375 , 11,664.625) up to three decimals
Nearest whole number
(11,629 , 11,665)
Step-by-step explanation:
<u>Explanation</u>:-
A sample of 7 adult elephants had an average weight of 11,647 pounds
size of the sample 'n' =7
The mean of the sample x⁻ = 11,647 pounds
The standard deviation of the sample 'S' = 24 pounds
<u>Step(ii):</u>-
The 95 % confidence interval of the population mean for the weights of adult elephants
![(x^{-} - t_{0.95} \frac{S}{\sqrt{n} } , x^{-} + t_{0.95} \frac{S}{\sqrt{n} } )](https://tex.z-dn.net/?f=%28x%5E%7B-%7D%20-%20t_%7B0.95%7D%20%5Cfrac%7BS%7D%7B%5Csqrt%7Bn%7D%20%7D%20%2C%20x%5E%7B-%7D%20%2B%20t_%7B0.95%7D%20%5Cfrac%7BS%7D%7B%5Csqrt%7Bn%7D%20%7D%20%29)
The degrees of freedom γ =n-1 = 7-1=6
t₆ = 1.943
![(11,647 - 1.943 \frac{24}{\sqrt{7} } , 11,647 + 1.943 \frac{24}{\sqrt{7} } )](https://tex.z-dn.net/?f=%2811%2C647%20-%201.943%20%5Cfrac%7B24%7D%7B%5Csqrt%7B7%7D%20%7D%20%2C%2011%2C647%20%2B%201.943%20%5Cfrac%7B24%7D%7B%5Csqrt%7B7%7D%20%7D%20%29)
(11,647-17.625 , 11,647+17.625)
(11,629.375 , 11,664.625)
<u>Conclusion</u>:-
The 95 % confidence interval of the population mean for the weights of adult elephants
(11,629 , 11,665)