The point estimate of the mean conversation length is the sample mean,Originally Posted by bombo31
so in this case it is 8.5 minutes. The margin of error of this estimate is
usually the standard error (SE) of the mean which is the population standard
deviation (SD) divided by the square root of the sample size. But we usually
use the sample SD as we don't know the population SD.
Now the problem you are given a variance (which is the square of the SD)
but with units of minutes - its units should be minutes squared. But let's
assume that this is a typo and the variance is 9 minutes squared, so the
SD is 3 minutes. Then the SE of the mean is 3/sqrt(45)~=0.447 minutes.
So your point estimate of the mean conversation length is 8.5 minutes with
a standard error of ~=0.477 minutes.