Mathematics and Statistics

Confidence Interval

A range, computed from a sample, that contains the true population value with a stated confidence.

A confidence interval on a mean is the sample mean plus or minus a critical value times the standard error, s/√n. When the population standard deviation is known, the critical value comes from the normal distribution (1.96 for 95%); when it is estimated from the sample, it comes from the t distribution with n − 1 degrees of freedom, which gives a wider interval for small samples.

The interval narrows as the sample grows, but only with the square root of n: four times the tests halve the width. A 95% interval does not mean a 95% chance that the true value lies inside this particular interval; it means that 95% of intervals built this way would contain it.

How much of the FE Civil exam is Mathematics and Statistics?