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About this document
- Pages
- 22 pages
- Price
- $22 one-time, yours to keep
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- Format
- Subject
- Mathematics, Statistics
- Module
- Chapter 6
This document covers the concept of sampling distributions in statistics, explaining population and sampling distributions, the sampling distribution of the sample mean, and sampling from normally and not normally distributed populations. It includes examples and formulas to illustrate these concepts. It is Chapter 6 of a course on elementary statistics.
What's inside
- Definition of population and sampling distributions
- Sampling distribution of the sample mean
- Sampling from normally distributed populations
- Sampling from not normally distributed populations
- Application of the sampling distribution of the sample mean
Who it is for: Students taking a course in elementary statistics. (Undergraduate)
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Summary
Sampling distributions show how sample statistics vary. Students learn how to calculate and use them, with examples and formulas.
Population and sampling distributions
The population distribution is the probability distribution of all data in a population. The sampling distribution is the probability distribution of a sample statistic, like the mean. It shows how sample means vary across all possible samples.
Sampling from a normally distributed population
When sampling from a normally distributed population, the sampling distribution of the mean is also normal. For large sample sizes, the sampling distribution of the mean is approximately normal, regardless of the population distribution.
Application of the sampling distribution
The sampling distribution of the mean can be used to calculate probabilities. For example, it can help find the probability that a sample mean is less than a certain value. The z value for a sample mean is calculated using a specific formula.
Other types of sampling distributions
The sampling distribution for the difference between means has specific properties. It can be used to calculate probabilities for the difference between sample means. The sampling distribution of the sample proportion is also covered.
Key terms
- Population distribution
- The probability distribution of all data in a population.
- Sampling distribution
- The probability distribution of a sample statistic.
- Standard error of the mean
- The standard deviation of the sampling distribution of the mean.
- Finite population correction factor
- A factor used in the standard error formula when the population size is finite.
- Sample proportion
- The proportion of a sample that has a certain characteristic.
- Population proportion
- The proportion of a population that has a certain characteristic.
Questions this document helps with
- What is the difference between population and sampling distributions?
- How do you calculate the standard error of the mean?
- When is the sampling distribution of the mean approximately normal?
Summary written with AI from the document's text.
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