STAT 301 Lecture Notes - Central Limit Theorem, Sampling Distribution, Point Estimation
Document Summary
The sampling distribution of the sample mean is a probability distribution consisting of all the sample means of a given sample size selected from a population. We don"t know the distribution of the population, or we know it"s not normal. Sampling distribution of x is normal if n is large . Properties of the sampling distribution of x x is the mean of the observations in a random sample of size n, from a population with mean and standard deviation . The mean of the distribution of x is x and the standard distribution is x. When n is significantly large, the sampling distribution of x is approximately normal (by central limit theorem) Regardless of the shape of the population distribution, the shape of the sampling distribution of the sample mean approaches a normal distribution as n increases. As n increases, the normal approximation of the sample distribution of x gets better.
