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Sampling Distribution, Reference: https://online.stat.psu.edu/, Harinaldi…
Sampling Distribution
The need of sampling
sampling are usually used for : to know the parameter of a population. And to determine what is the different from a two sampel which one is the most significant
The finite and infinite distribution difference are on their population. The finite are countable, while infinite have to many population until infinity
Random Sampling
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Random sample will be formed if : 1. Xi are free in a statistic way, 2. each Xi follow the probability distribution function that organized the population
DEFINITION: A sampling distribution is a probability distribution of a statistic obtained from a larger number of samples drawn from a specific population.
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The sampling distribution of a given population is the distribution of frequencies of a range of different outcomes that could possibly occur for a statistic of a population.
Central Limit theorem
The central limit theorem states that if you have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement text,
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Of the variance
Follow the theorem:1. X1,X2,X3,...are observations of a random sample of size n from the normal distribution N(μ,σ^2)
is the sample mean of the n observations, and
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Benefits
knowing the degree to which means from different samples differ from each other and from the population mean would give you a sense of how close your particular sample mean is likely to be to the population mean
Lack of Bias
Because individuals who make up the subset of the larger group are chosen at random, each individual in the large population set has the same probability of being selected.
This creates, in most cases, a balanced subset that carries the greatest potential for representing the larger group as a whole
Simplicity
producing a simple random sample is much less complicated than other methods, such as stratified random sampling. As mentioned, individuals in the subset are selected randomly and there are no additional steps
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