To find the standard deviation from the given standard error and sample size, we can follow these steps:
1. Understand the Relationship: Recall that the standard error (SE) of a sample mean is related to the standard deviation (SD) of the sample by the formula:
[tex]\[
SE = \frac{SD}{\sqrt{n}}
\][/tex]
where [tex]\( n \)[/tex] is the sample size.
2. Rearrange the Formula: To find the standard deviation, rearrange the formula to solve for [tex]\( SD \)[/tex]:
[tex]\[
SD = SE \times \sqrt{n}
\][/tex]
3. Substitute the Given Values:
- The sample size [tex]\( n \)[/tex] is 80.
- The standard error [tex]\( SE \)[/tex] is approximately 0.595.
Now, substitute these values into the formula:
[tex]\[
SD = 0.595 \times \sqrt{80}
\][/tex]
4. Calculate the Square Root: The square root of 80 is approximately 8.944.
5. Perform the Multiplication: Multiply the standard error by the square root of the sample size:
[tex]\[
SD = 0.595 \times 8.944 \approx 5.321841786449499
\][/tex]
6. Round to the Nearest Hundredth: Finally, round the result to the nearest hundredth (two decimal places):
[tex]\[
SD \approx 5.32
\][/tex]
Therefore, the standard deviation is approximately 5.32.
