Standard Error Statistics Example 1

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Example 1

easy
A population has a standard deviation of ฯƒ=20\sigma = 20. If you take a random sample of n=100n = 100, what is the standard error of the sample mean?

Solution

  1. 1
    Step 1: The standard error (SE) of the sample mean is given by SE=ฯƒnSE = \frac{\sigma}{\sqrt{n}}.
  2. 2
    Step 2: SE=20100=2010=2SE = \frac{20}{\sqrt{100}} = \frac{20}{10} = 2.
  3. 3
    Step 3: This means the sample mean is expected to vary by about 2 units from the true population mean across different samples of size 100.

Answer

SE=2SE = 2.
The standard error measures the precision of the sample mean as an estimate of the population mean. It decreases as sample size increases, meaning larger samples give more precise estimates. The SE is the standard deviation of the sampling distribution of the mean.

About Standard Error

The standard error (SE) is the standard deviation of a sampling distribution, measuring how much a sample statistic (like the sample mean) typically varies from the true population parameter across repeated samples. It decreases as sample size increases.

Learn more about Standard Error โ†’

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