Standard Error Statistics Example 3

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Example 3

medium
A researcher measures the reaction time of 64 participants and finds a sample standard deviation of s=40s = 40 ms. Calculate the standard error and construct an approximate 95% confidence interval if the sample mean is 250 ms.

Solution

  1. 1
    Step 1: SE=sn=4064=408=5SE = \frac{s}{\sqrt{n}} = \frac{40}{\sqrt{64}} = \frac{40}{8} = 5 ms.
  2. 2
    Step 2: 95% CI โ‰ˆxห‰ยฑ2ร—SE=250ยฑ10\approx \bar{x} \pm 2 \times SE = 250 \pm 10, giving (240,260)(240, 260) ms.

Answer

SE=5SE = 5 ms. 95% CI: approximately (240 ms, 260 ms).
When the population standard deviation is unknown, we use the sample standard deviation to estimate the standard error. The 95% confidence interval is approximately the sample mean plus or minus 2 standard errors, providing a range likely to contain the true population 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.

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