Many statisticians recommend using trimmed means to estimate a population mean yU if there are outliers. The procedure used to find an α-trimmed mean in an SRS of size n is to remove the largest nα observations and the smallest nα observations, and then calculate the mean of the n(1 − 2α) observations that remain. Show that the α-trimmed mean for a finite population U of N observation units is

Where q1 and q2 are the α and (1−α) quantiles, respectively. Now propose an estimator of the population α-trimmed mean for data from a complex survey using ˆF(y) and ˆf (y).