Answer to Question #311148 in Statistics and Probability for john

Question

The following are the age of 8 jeepney passengers in a waiting shed: 12, 15, 18, 19, 21, 23, 35, and 40. A sample with size 7 is chosen to ride in the current jeepney. Find the standard error of the sample mean.

Answer 1

$n=7\\EX=\frac{1}{8}\left( 12+15+18+19+21+23+35+40 \right) =22.875\\EX^2=\frac{1}{8}\left( 12^2+15^2+18^2+19^2+21^2+23^2+35^2+40^2 \right) =606.125\\\sigma ^2=EX^2-\left( EX \right) ^2=606.125-22.875^2=82.8594\\s\left( \bar{x} \right) =\frac{\sigma}{\sqrt{n}}=\frac{\sqrt{82.8594}}{\sqrt{7}}=3.4405$