Question

A sample of 7 adult elephants had an average weight of 12,572 pounds. The standard deviation for the sample was 26 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

`CI=(12553<\mu<12591)`

Step-by-step explanation

The confidence interval formula is given by

`\begin{gathered} CI=\bar{x}\pm z\frac{s}{\sqrt[]{n}} \\ \text{Where;} \\ CI\text{ is the 95 percent confidence interval} \\ \bar{x}\text{ is the average weight }=12572 \\ z\text{ is the confidence value }=1.96 \\ s\text{ is the sample standard deviation }=26 \\ n\text{ is the sample size }=7 \end{gathered}`

This implies that

`\begin{gathered} CI=12572\pm1.96(\frac{26}{\sqrt[]{7}}) \\ CI=12572\pm(50.960)/(2.646) \\ CI=12572\pm19.259 \\ CI=(12552.741,12591.259) \\ CI=(12553<\mu<12591) \end{gathered}`

The 95% confidence interval of the population mean for the weights of adult elephants is (12553 < μ < 12591)