Question

Given a standard deviation of 3.5 and a sample size of 5, what is the standard error? Round to the nearest hundredth

Answer 1

The standard error (SE) is calculated using the formula:

\[
SE = \frac{s}{\sqrt{n}}
\]

where \( s \) is the standard deviation and \( n \) is the sample size.

Given:
- Standard deviation (\( s \)) = 3.5
- Sample size (\( n \)) = 5

Now plug the values into the formula:

\[
SE = \frac{3.5}{\sqrt{5}}
\]

First, calculate \( \sqrt{5} \):

\[
\sqrt{5} \approx 2.236
\]

Now, calculate the standard error:

\[
SE = \frac{3.5}{2.236} \approx 1.566
\]

Rounding to the nearest hundredth, the standard error is:

\[
SE \approx 1.57
\]

So, the standard error is approximately **1.57**.