Sampling Distribution Math Example 3

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Example 3

easy
The standard error of a sample mean is ฯƒXห‰=ฯƒn\sigma_{\bar{X}} = \frac{\sigma}{\sqrt{n}}. If ฯƒ=10\sigma=10 and n=100n=100, find the standard error. What happens to the SE if n is quadrupled to 400?

Solution

  1. 1
    n=100n=100: SE=10100=1010=1SE = \frac{10}{\sqrt{100}} = \frac{10}{10} = 1
  2. 2
    n=400n=400: SE=10400=1020=0.5SE = \frac{10}{\sqrt{400}} = \frac{10}{20} = 0.5
  3. 3
    Quadrupling nn halved the SE โ€” SE decreases by 4=2\sqrt{4} = 2 factor

Answer

SE(n=100) = 1; SE(n=400) = 0.5. Quadrupling n halves the standard error.
Standard error decreases as 1/โˆšn. To halve the standard error (double precision), you must quadruple the sample size. This is why large sample sizes are expensive: each improvement requires 4ร— more data.

About Sampling Distribution

The probability distribution of a statistic (such as the sample mean) computed from all possible random samples of the same size drawn from a population.

Learn more about Sampling Distribution โ†’

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