Question

Weights of Elephants A sample of 7 adult elephants had an average weight of 11,647 pounds. The standard deviation for the sample was 24 pounds. Find the 95 % confidence interval of the population mean for the weights of adult elephants. Assume the variable is normally distributed. Round intermediate answers to at least three decimal places. Round your final answers to the nearest whole number.

Answer 1

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:

Explanation:-

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

Step(ii):-

The 95 % confidence interval of the population mean for the weights of adult elephants

$(x^{-} - t_{0.95} \frac{S}{\sqrt{n} } , x^{-} + t_{0.95} \frac{S}{\sqrt{n} } )$

The degrees of freedom γ =n-1 = 7-1=6

t₆ = 1.943

$(11,647 - 1.943 \frac{24}{\sqrt{7} } , 11,647 + 1.943 \frac{24}{\sqrt{7} } )$

(11,647-17.625 , 11,647+17.625)

(11,629.375 , 11,664.625)

Conclusion:-

The 95 % confidence interval of the population mean for the weights of adult elephants

(11,629 , 11,665)