Sampling Distribution Statistics Example 2

Follow the full solution, then compare it with the other examples linked below.

Example 2

hard
Why does increasing the sample size from 25 to 100 improve the precision of a sample mean?

Solution

  1. 1
    Step 1: With n=25n = 25: SE=ฯƒ25=ฯƒ5\text{SE} = \frac{\sigma}{\sqrt{25}} = \frac{\sigma}{5}.
  2. 2
    Step 2: With n=100n = 100: SE=ฯƒ100=ฯƒ10\text{SE} = \frac{\sigma}{\sqrt{100}} = \frac{\sigma}{10}.
  3. 3
    Step 3: The standard error halves, meaning sample means are twice as precise (clustered twice as tightly around ฮผ\mu).

Answer

Quadrupling the sample size halves the standard error, doubling precision.
Precision improves with the square root of the sample size. To halve the standard error, you need to quadruple nn. This has practical implications for study design.

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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More Sampling Distribution Examples

Example 1 hard

A population has mean [formula] and standard deviation [formula]. If we take samples of size [formul

Example 3 hard

A population has [formula]. Find the standard error for sample sizes [formula] and [formula].

Example 4 hard

A population has mean [formula] and standard deviation [formula]. For samples of size [formula], wha

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