In this problem, a data set of size 5 consists of the numbers 1 through 5; a data set of size 6 consists of the numbers 1 through 6; and so on.
(a) For data sets of size 5 and 6, compute the complete randomization distribution for the mean of samples of size 3. (There will be 10 and 20 members respectively in the two distributions.) How normal do these distributions look?
(b) For data sets of size 4 and 5, compute the complete randomization distribution for the mean of samples of any size (size 1, size 2, . . ., up to all the data in the sample). Again, compare these to normal.
(c) Compare the size 5 distributions from parts a) and b). How do they compare for mean, median, variance, and so on.