Sampling Distributions and the central limit theorem

sampling distribution of a statistic

the distribution of all possible values that can be assumed by some statistic, computed from samples of the same size, randomly drawn from the same population

sampling distribution of the same mean

a distribution, or list, of all possible values of the sample mean, x bar, given a specific sample size

2 properties of sampling distribution of sample mean, x bar

1. µ_x̄= µ

2. σ = σ/(√n)

example of standard deviation of the sampling distribution of the sample mean

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central limit theorem

The Central Limit Theorem states that the average of a large number of independent, random variables approaches a normal (bell-shaped) distribution, regardless of the original variable's distribution

in the CLT, what does the mean of all sample means equal

the population mean

in CLT, what does the standard deviation of all sample mean turn into

the standard error of the mean

Formula for applying the CLT to an individual value

applying the CLT to a sample or group

apply the CLT to a sample

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apply the CLT to a group

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mean in a distribution in a sampling distribution of a sample proportion

μp̂ is the average of all the possible sample proportions and is equal to the true population proportion

standard deviation in a sampling distribution of the sample proportion formula

what does p hat represent

the sample proportion

what does p represent

the population proportion

what does n represent

the sample size

sampling distribution of the sample proportion example

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