Sampling Distribution Statistics Example 4

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

Example 4

hard
A population has mean ฮผ=120\mu = 120 and standard deviation ฯƒ=24\sigma = 24. For samples of size n=36n = 36, what are the mean and standard error of the sampling distribution of xห‰\bar{x}?

Solution

  1. 1
    Step 1: The sampling distribution of xห‰\bar{x} has mean equal to the population mean, so its mean is 120120.
  2. 2
    Step 2: The standard error is ฯƒn=2436=246=4\frac{\sigma}{\sqrt{n}} = \frac{24}{\sqrt{36}} = \frac{24}{6} = 4.

Answer

Mean = 120120 and standard error = 44.
Sampling distributions describe how sample means vary from sample to sample. The center stays at the population mean, while the spread shrinks according to the standard error formula.

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.

Learn more about Sampling Distribution โ†’

More Sampling Distribution Examples

Example 1 hard

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

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].

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