Definition
It is a specific type of Sampling Distribution
Let be a probability function , mean and variance , then the Sampling Distribution of the mean is:
Normal Approximation
Independence
For a sufficiently large , we can apply the Central Limit Theorem
This applies when:
- has a Normal Distribution
No Independence
When the population is finite and we have a Sampling without replacement, then we follow a Hypergeometric Distribution.
And therefore:
Solution Methods
Normal Population
In R:
pnorm(x, μ, σ/sqrt(n))Normal Population, n > 30, but sigma unknown
In R:
t_calc = (smu - mu) / (S / sqrt(n))
pt(t_calc, df = n-1)