CFA-Central limit theorem

1.Central limit theorem and standard error

1.1 Central limit theorem

Given a population described by any probability distribution having mean and finite variance,the sampling distribution of the sample mean,computed from samples of size n from this population,will be approximatly normal with mean (the population mean) and variance (the population variance divided by n)when the sample size n is large.

1.2 Standard error

The standard deviation of the distribution of sample statistic(sampling distribution)

Standard error of sample mean:the standard deviation of the distribution of sample means.

2.Confidence interval for population mean and reliability factors.

2.1 Confidence interval for population mean

A range that contain the population mean with a given confidence level .

The central limit theorem can be used to construct confidence intervals for population means.

Confidence interval of population means

=point estimate of population mean +-Reliability factor *Standard error of sample mean