1. What is Standard Error?

Standard Error (SE) measures the precision of a sample mean estimate relative to the true population mean. It quantifies the variability between sample means if multiple samples were taken from the same population.

2. How Does the Calculator Work?

The calculator uses the standard error formula:

Where:

• \( s \) — Sample standard deviation
• \( n \) — Sample size

Explanation: The standard error decreases as sample size increases, indicating greater precision in estimating the population mean.

3. Importance of Standard Error

Details: Standard error is crucial for constructing confidence intervals and conducting hypothesis tests. It helps determine how much the sample mean is likely to vary from the true population mean.

4. Using the Calculator

Tips: Enter the sample standard deviation and sample size. Both values must be positive numbers (standard deviation > 0, sample size ≥ 1).

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between standard deviation and standard error?
A: Standard deviation measures variability within a sample, while standard error measures the precision of the sample mean estimate.

Q2: How does sample size affect standard error?
A: As sample size increases, standard error decreases, providing a more precise estimate of the population mean.

Q3: When should I use standard error?
A: Use standard error when constructing confidence intervals or conducting hypothesis tests about population means.

Q4: Can standard error be zero?
A: Standard error approaches zero as sample size approaches infinity, but in practice, it's never exactly zero with finite samples.

Q5: How is standard error related to confidence intervals?
A: Confidence intervals are typically constructed as: mean ± (critical value × standard error).