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Population, Sample, and SamplingStats 2020. 1. 11. 14:59
1. Overview
How to select good random samples from the population
How to calculate the estimate of a population mean using samples
How can I assure that the sample will provide adequate information about the population parameters
2. Description
2.1 Simple Random Sampling Method
2.1.1 finite population
A simple random sample of size n from a finite population of size N is a sample selected such that:
- Every observation has an equal chance of being selected
- Every sample of n observation has an equal chance of being selected
2.1.2 infinite population
Select a random sample such that each element is selected independently: Avoid selection bias
2.2 Point estimators
To estimate population parameters we compute sample parameters
2.2.1 Standard Deviation
If the sample size is less than or equal to 5% of the population size $\frac{n}{N}\leq 0.05$:
$$\sigma _{\bar{x}}=\frac{\sigma }{\sqrt{n}}$$
If the sample size is greater than 5% of the population size $\frac{n}{N}$>0.05:
$$\sigma _{\bar{x}}=\frac{\sqrt{N-n}}{\sqrt{N-1}}\frac{\sigma }{\sqrt{n}}$$
where $\frac{\sqrt{N-n}}{\sqrt{N-1}}$ is finite population correction factor
2.3 Sampling Error
The standard error is a measure of the sampling error of the sampling distribution. There are others, but standard error is, by far, the most commonly used when dealing with survey data.
$$STDERR=\frac{\sigma}{\sqrt{n}}$$
$$STDERR=\sqrt{\frac{p*(1-p)}{n}}$$
you can see other formulas within this link
2.4 Central Limit Theorem
The sampling distribution of the mean of a random sample drawn from any population is approximately normal for a sufficiently large sample size. The larger the sample size, the more closely the sampling distribution of $\bar{x}$ will resemble a normal distribution.
2.5 Degree of freedom
3. Reference
https://www.youtube.com/watch?v=92s7IVS6A34
https://statisticsbyjim.com/hypothesis-testing/degrees-freedom-statistics/
https://www.investopedia.com/terms/t/tdistribution.asp
https://corporatefinanceinstitute.com/resources/knowledge/other/kurtosis/
https://en.wikipedia.org/wiki/Central_limit_theorem
https://www.en-net.org/question/768.aspx
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