A simple random sample of 40 items resulted in a sample mean of 25. The population standard deviation is σ = 5.

What is the standard error of the mean, σxbar?

The standard error of the mean (denoted as \(\sigma_{\bar{x}}\)) is calculated using the formula:

\[
\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}}
\]

Where:
- \(\sigma\) is the population standard deviation (\(5\)),
- \(n\) is the sample size (\(40\)).

### Calculation:
\[
\sigma_{\bar{x}} = \frac{5}{\sqrt{40}}
\]

First, calculate \(\sqrt{40}\):
\[
\sqrt{40} \approx 6.3246
\]

Now divide:
\[
\sigma_{\bar{x}} = \frac{5}{6.3246} \approx 0.7906
\]

### Final Answer:
The standard error of the mean is approximately **0.791**.

Would you like more explanation or have any further questions?

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### Related Questions:
1. How is the standard error of the mean different from the population standard deviation?
2. What happens to the standard error if the sample size increases?
3. How would the result change if the population standard deviation were unknown?
4. Why is it important to use the sample size in calculating the standard error of the mean?
5. Can the standard error be used to construct a confidence interval?

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### Tip:
When calculating the standard error, always verify whether the standard deviation provided is for the population (\(\sigma\)) or the sample (\(s\)), as they involve different treatments in the formulas.

A simple random sample of 40 items resulted in a sample mean of 25. The population standard deviation is σ = 5. What is the standard error of the mean, σxbar?

Learn how to calculate the standard error of the mean for a sample size of 40 with a population standard deviation of 5. This problem illustrates the formula σx̄ = σ / √n and shows the step-by-step solution. Suitable for students in Grades 10-12.

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