95% confidence intervals

• Mar 21st 2014, 06:09 AM
alexlbrown59
95% confidence intervals
I have data that is very right skew where I know the sample mean, the sample standard deviation and the sample size. I have calculated a 95% confidence interval for the mean using the following method:
(mean-1.96xESE, mean+1.96xESE) where ESE is estimated standard error.
The question then asks why it doesn't matter whether the distribution of the population is or isn't normal?

Does anyone know the answer? Thanks.
• Mar 21st 2014, 06:56 AM
Shakarri
Re: 95% confidence intervals
The central limit theorem states that when taking samples from a distribution with mean $\displaystyle \mu$ and variance $\displaystyle \sigma^2$ the distribution of the sample tends toward a normal distribution with mean $\displaystyle \mu$ and variance $\displaystyle \frac{\sigma^2}{n}$ as sample size n increases. In the limit as n tends to infinity the sample mean is exactly normally distributed. For large sample sizes (n>30 or n>50) we often assume that the distribution is normal.
Central limit theorem - Wikipedia, the free encyclopedia