Question

Let the population be given by the numbers {-2,-1,0,1,2}. Take all random samples of size 3 without replacement and obtain the sampling distribution of the sample mean.

[10 Marks]

Answer 1

Solution:

We are given the population valuess as {-2,-1,0,1,2} population size N=5 and sample size n=3. Thus, the number of possible samples which can be drawn without replacement is

This is for taking 2 samples

The sampling distribution of the sample mean is

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Sample Sample Sample Sample Sample Sample Sample Sample No. Values Mean No. Values Mean 1 -1.5 -1 0 -1 7 0.5 N -2 -2,-1 -2,0 -2,1 -2,2 -1,0 8 -1,1 -1,2 0,1 0,2 1, 2 -0.5 0 0.5 4 1 0 10 5 -0.5 1.5

x_barf -1.5 f(x_bar) x_bar*f(x_bar) 0.10 0.1 1 -1 1 0.10 0.1 -0.5 2 0.4 0.20 0.20 0 2 0.4 0.5 2 0.10 0.2 1 1 0.10 0.1 1.5 1 0.10 0.1 10

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For 3 samples

Sample no.	Sample Values	Sample Mean	Sample no.	Sample Values	Sample Mean
1	-2,-1,0	-1	6	0,1,2	1
2	-2,-1,1	-2/3	7	-2,0,1	-1/3
3	-2,-1,2	-1/3	8	-2,0,2	0
4	-1,0,1	0	9	-1,1,2	2/3
5	-1,0,2	1/3	10	-2,1,2	1/3

The sampling distribution of the sample mean is

X_bar	f	f(x_bar)	x_bar*f(xbar)
-1	1	0.1	0.1
-2/3	1	0.1	0.1
-1/3	2	0.2	0.4
0	2	0.2	0.4
1/3	2	0.2	0.4
2/3	1	0.1	0.1
1	1	0.1	0.1