Which of the following correctly expresses a confidence interval for a population mean in the standard form?

• A. $x\pm z\cdot n$
• B. $x\pm s$
• C. $x\pm z\cdot \frac{s}{\sqrt{n}}$
• D. $x+z\cdot s$

Answer: (C)

Verified step by step guidance

1. Understand that a confidence interval for a population mean is generally expressed as the sample mean plus or minus a margin of error.
2. Recognize that the margin of error is calculated by multiplying a critical value (often denoted as \(z\) for known population standard deviation or \(t\) for unknown) by the standard error of the mean.
3. Recall that the standard error of the mean is the sample standard deviation \(s\) divided by the square root of the sample size \(n\), expressed as \(\frac{s}{\sqrt{n}}\).
4. Combine these components to write the confidence interval in the standard form: \(x \pm z \cdot \frac{s}{\sqrt{n}}\), where \(x\) is the sample mean, \(z\) is the critical value, \(s\) is the sample standard deviation, and \(n\) is the sample size.
5. Note that the other options either omit the division by \(\sqrt{n}\) or do not include the margin of error correctly, so they do not represent the standard form of a confidence interval for a population mean.