I am working out confidence intervals and was wondering what effect knowing the variance of the distribution has on the interval.
I know that if i know the variance I am going to use the z distribution as opposed to the t distribution but why would it make a difference on the confidence intervals and which one would i prefer to use??
In general (I'm tempted to say "always"), the more details you know about a set of data, the stronger your confidence about any claims you make.
The t distribution curve has a similar shape to the Z curve (both bell-shaped) but is flatter (i.e. has "more" probability at the extremes). Have a look at wikipedia.
What impact do you think that will have on confidence intervals?
(Original post by masterasg)
sof the t disttttbuion curve is flatter, then the confidence intervals will be wider, but why then would i be using the t distribution for the first one, could i not use the z distribution for both?
Because those are different situations. The theoretical model upon which the normal distribution is based requires the variance of the population to be known, whereas the model the t distribution is built on only requires an estimate of the population variance from a sample of known size.