Questions: What is the standard deviation of the sample means called? What is the formula for this standard deviation? The standard error of the mean: σ/√n

What is the standard deviation of the sample means called? What is the formula for this standard deviation? The standard error of the mean: σ/√n
Transcript text: What is the standard deviation of the sample means called? What is the formula for this standard deviation? The standard error of the mean: $\frac{\sigma}{\sqrt{n}}$
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Solution

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Solution Steps

The standard deviation of the sample means is called the standard error of the mean. The correct formula for the standard error of the mean is \(\frac{\sigma}{\sqrt{n}}\), where \(\sigma\) is the population standard deviation and \(n\) is the sample size.

Step 1: Identify the Standard Error of the Mean

The standard error of the mean (SEM) is defined as the standard deviation of the sample means. It quantifies how much the sample mean is expected to vary from the true population mean.

Step 2: Apply the Formula

The formula for the standard error of the mean is given by:

\[ SEM = \frac{\sigma}{\sqrt{n}} \]

where:

  • \(\sigma = 10\) (the population standard deviation)
  • \(n = 25\) (the sample size)
Step 3: Calculate the Standard Error

Substituting the values into the formula:

\[ SEM = \frac{10}{\sqrt{25}} = \frac{10}{5} = 2.0 \]

Final Answer

The standard error of the mean is \\(\boxed{2.0}\\).

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