Confidence interval

HI, I have basic question on confidence interval. Here are two formulas for 99% degree of confidence x value = mean + 1.65 * Sigma x value = mean + 1.65 * sigma/ sqrt(n) We always use second formula to calculate confidence interval. I saw in sample exam a question on it and they used first formula. I would like to understand what makes to use first formula vs second one. In sample exam, they calculated interval by multiplying standard deviation by 3 times to get 99% confidence interval. This is bothering me for quiet some time. Appreciate any comments on understanding one vs other. Thanks, Chinni

Chinni I believe you are getting confused by a 90% confidence interval and a 99% confidence interval. For 90% --> z score is +/- 1.645 95% +/- 1.96 (sometimes +/- 2 is used) 99% +/- 2.58 (as a shortcut +/- 3 is used) sigma --> Population is given, and you are predicting the confidence interval for the population itself (around the mean). sigma / root(n) --> sample of size n is given, and you are predicting the CI for a sample mean. (remember the population may have more samples of size n that may be taken, hence – your sample standard deviation needs to be adjusted). CP

cpk123, Thanks for elaborate explanation. I have confused by giving 1.65 and referring to one of the sample problem that asked for confidence interval for 99% and they used 3 times standard deviation. Now I understood better. So, if population mean and population standard deviation are given then confidence interval for 90% level becomes x = population mean + 1.65 * population variance. So, there is no need to know the size of population in the above case. I am assuming second formula to to use Sigma/sqrt(n) is used only in case of samples.