Chapter 8.3, Problem 67E

To determine

To find: The standard error of the mean for the provided information.

Answer to Problem 67E

The standard error of the mean is 1.79.

Explanation of Solution

Given:

Sample mean $\left(\overline{x}\right)=114.9$

Sample standard deviation $\left(s_x\right)=9.3$

Sample size $\left(n\right)=27$

Formula used:

The formula to compute the standard error of mean is:

  $S{E}_{\overline{x}}=\frac{s_x}{\sqrt{n}}$

Where,

s is the sample standard deviation

The formula to compute the sample standard deviation is:

  $s=\sqrt{\frac{{\displaystyle \sum {\left(x-\overline{x}\right)}^2}}{n-1}}$

Calculation:

The standard error of the mean can be calculated as:

  $\begin{array}{c}S{E}_{\overline{x}}=\frac{s_x}{\sqrt{n}}\\ =\frac{9.3}{\sqrt{27}}\\ =1.79\end{array}$

The standard error of the mean is 1.79.