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Chapter 8: Sampling Methods (Sample (Cluster Sampling (A population is…
Chapter 8: Sampling Methods
Sample
Cluster Sampling
A population is divided into clusters using naturally occurring geographic or other boundaries. Then clusters are randomly selected and a sample is collected by randomly selecting from each class
Stratified Random
A population is divided into subgroups, called strata, and a sample is selected from each stratum
Systematic Random
The subjects of the population are arranged in some order. A random starting point is selected and then every kth member of the population is selected for the sample
Simple Random
A sample selected so that each subject in the population has the chance of being included
Probability Sample
A sample selected such that each subjects in the population being studied has a known likelihood of being included in the sample
Sampling Distribution of the Sample Mean
A probability distribution consisting of all possible sample means of a given sample size selected from a population
Formula
Central Limit Theorem
If all samples of a particular size are selected from any population, the sampling distribution of the sample mean is approximately a normal distribution.
Characteristic
If the population follows a normal distribution, then the sample mean will be normal
If the population is symmetrical, the shape will emerge as normal with samples as small as 10
If a distribution that is skewed or has thick tails, it may require 30 samples or more to observe normality feature
Condition
If Sigma is Known
If population follows the normal distribution, sample mean will follow normal distribution
If the shape is known to be non-normal, but the sample contains 30 observations, sample means follow normal distribution
Formula
If Sigma is Unknown, or Population is Non-Normal
If population does not follow the normal distribution, but the sample contains 30 observations, the sample mean will follow the normal distribution
Formula