It is well-known that the traditional t procedure for estimating a single mean can have poor performance in the presence of outliers. Suppose you propose a new procedure called "trim-4" where one first trims the two smallest and two largest observations from the data, and then construct the usual t interval based on the remaining n-4 observations. You are interested in exploring properties of this new method of estimating a population mean.
(a) Explicitly define your new confidence procedure including the choice of critical values.
(b) Suppose one samples from a normal distribution with mean and standard deviation a. Describe how you would use a Monte Carlo procedure to find the probability of coverage of your new confidence procedure.
(c) Using some type of variance reduction, describe an improved Monte Carlo experiment to estimate the probability of coverage.
Give as many details of the experiment us possible, and explain how you would measure the size of the variance reduction.