Practice Sampling Distribution in Statistics

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

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

If you took 1000 different random samples and calculated the mean of each, those 1000 means would form a distribution. That's the sampling distribution - it shows how sample statistics vary.

Example 1

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

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 \sigma = 20. Find the standard error for sample sizes n = 16 and n = 64.

Example 4

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