Sampling Distribution Statistics Example 1

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Example 1

hard
A population has mean ฮผ=60\mu = 60 and standard deviation ฯƒ=12\sigma = 12. If we take samples of size n=36n = 36, what is the standard error of the sample mean?

Solution

  1. 1
    Step 1: The standard error is SE=ฯƒn\text{SE} = \frac{\sigma}{\sqrt{n}}.
  2. 2
    Step 2: SE=1236=126=2\text{SE} = \frac{12}{\sqrt{36}} = \frac{12}{6} = 2.
  3. 3
    Step 3: The sampling distribution of xห‰\bar{x} has mean 60 and standard error 2.

Answer

SE=2\text{SE} = 2
The standard error measures the variability of sample means. As sample size increases, the standard error decreases, meaning sample means cluster more tightly around the population mean.

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 2 hard

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

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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