Someone helps? i want to know the functions for solving this problem. thanx?

Question

A population consists of the following six values: 15, 20, 12, 18, 24, and 25. Find the sampling distribution of the mean for all samples of size 4. Then use this sampling distribution to compute the mean of the sampling distribution. What is the relationship between the mean of the population and the mean of the sampling distribution? Verify your answer to the previous question with actual calculations. Also compute the standard error of the mean and the variance of the sampling distribution of Xbar.

Answer 1

for the samples of size 4, you just have to get every combination of six choose four.  then, take the mean of each set of four for the sample mean.  then take the mean of all sample means to get the distribution mean.  you'll find that they're both 19.  no magic - just a lot of number crunching.

in matlab:

>> pop = [15 20 12 18 24 25];

>> nchoosek(pop,4)

ans =

    15    20    12    18

    15    20    12    24

    15    20    12    25

    15    20    18    24

    15    20    18    25

    15    20    24    25

    15    12    18    24

    15    12    18    25

    15    12    24    25

    15    18    24    25

    20    12    18    24

    20    12    18    25

    20    12    24    25

    20    18    24    25

    12    18    24    25

>> mean(nchoosek(pop,4),2)

ans =

   16.2500

   17.7500

   18.0000

   19.2500

   19.5000

   21.0000

   17.2500

   17.5000

   19.0000

   20.5000

   18.5000

   18.7500

   20.2500

   21.7500

   19.7500

>> mean(mean(nchoosek(pop,4),2))

ans =

    19