CFA-Central|CFA-Central limit theorem
【CFA-Central|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
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