Sampling Distribution Statistics Example 3

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Example 3

hard
A population has ฯƒ=20\sigma = 20. Find the standard error for sample sizes n=16n = 16 and n=64n = 64.

Solution

  1. 1
    Step 1: For n=16n = 16: SE=2016=204=5\text{SE} = \frac{20}{\sqrt{16}} = \frac{20}{4} = 5.
  2. 2
    Step 2: For n=64n = 64: SE=2064=208=2.5\text{SE} = \frac{20}{\sqrt{64}} = \frac{20}{8} = 2.5.

Answer

SE = 5 (n=16), SE = 2.5 (n=64).
Quadrupling the sample size (16 to 64) halves the standard error (5 to 2.5), illustrating the square-root relationship between sample size and precision.

About Sampling Distribution

The sampling distribution is the probability distribution of a statistic (such as the sample mean xห‰\bar{x}) computed from all possible random samples of a given size nn drawn from a population. It describes how that statistic varies from sample to sample.

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