Sampling Distributions and Central Limit Theorem
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This document discusses different sampling methods including simple random sampling, stratified random sampling, and cluster sampling. It also covers key concepts related to sampling distributions including the central limit theorem. Specifically, it states that the sampling distribution of the sample mean will be normally distributed if the population is normally distributed or if the sample size is at least 30, even if the population is not normally distributed. It also notes that the mean of the sampling distribution is equal to the population mean and its variance is equal to the population variance divided by the sample size.
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Denis is a dynamic and results-driven Chief Information Officer (CIO) with a distinguished career spanning information systems analysis and technical project management. With a proven track record of spearheading the design and delivery of cutting-edge Information Management solutions, he has consistently elevated business operations, streamlined reporting functions, and maximized process efficiency.
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Date: May 29, 2024
Tags: Information Security, ISO/IEC 27001, ISO/IEC 42001, Artificial Intelligence, GDPR
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Training: ISO/IEC 27001 Information Security Management System - EN | PECB
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9
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"Learn about all the ways Walmart supports nonprofit organizations.
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Sampling Distributions and Central Limit Theorem
- 2. Simple Random Sample Systematic Random Sampling Stratified Random Sampling Cluster Sampling
- 3. Simple Random Sample: A sample selected so that each item or person in the population has the same chance of being included. Stratified Random Sampling: A population is first divided into subgroups, called strata, and a sample is selected from each stratum. Useful when a population can clearly be divided in groups based on some characteristics.
- 4. Cluster Sampling: A population is divide into clusters using naturally occurring, geographic, or other kinds of boundaries. Then, clusters are randomly selected and a sample is collected by randomly selecting from each cluster. The sampling error is the difference between a sample statistic and its corresponding population parameter.
- 5. The sampling distribution of the sample mean is a probability distribution consisting of all possible sample means of a given sample size selected from a population.
- 6. For any sample size, the sampling distribution of the sample mean will also be normal if the population follows a normal probability distribution. If the population distribution is symmetrical (but not normal), the normal shape of the distribution of the sample mean emerges with samples as small as 10. If a distribution is skewed or has thick tails, it may require samples of 30 or more to observe the normality feature. The mean of the sampling distribution is equal to μ and the variance is equal to .
- 7. If is the mean of a random sample of size n from a normal population with the mean of μ and standard deviation of σ, the distribution of is a normal distribution with mean = μ and standard deviation A A .
- 8. 1. The mean of the distribution of sample means will be exactly equal to the population mean if we are able to select all possible samples of the same size from a given population. 2. There will be less dispersion in the sampling distribution of the sample mean than in the population. As the sample size increases, the standard error of the mean decreases.
- 10. If a population follows the normal distribution, the sampling distribution of the sample mean will also follow the normal distribution. If the shape is known to be non-normal, but the sample contains at least 30 observations, the central limit theorem guarantees the sampling distribution of the mean follows a normal distribution.
- 11. Sampling Distribution ◦ The central limit theorem holds, and the distribution is approximately normal if np > 5 and nq > 5 (p is the population proportion and q = 1 – p) ◦ The mean of the distribution is p. ◦ The variance of the distribution is pq / n