Question 1194616: Consider a population consisting of a values 2,4,6. List all the possible samples of size n=2 which can be drawn with replacement from the population. Describe the sampling distribution of the sample means. Compute for the mean and variance of the population. Find the mean, variance, and standard deviation of the sampling distribution of the sample means.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! there are 9 samples of size 2
22--mean2
24--mean 3
26--4
42--3
44--4
46--5
62--4
64--5
66--6
The mean of the sample means is 4
the variance is squared of the differences squared from the mean, added together, divided by 9
That is 12/9 The sd is the sqrt of that or 2 sqrt(3)/3.
The mean of the population is 4
the variance is 8/3, and the sd is sqrt(24)/3 or 2/3
The sampling distribution mean is the same as the population mean, 4.
The variance of the population is 8/3, and the variance of the sampling distribution is V(pop)/sample size, which is 8/(3*2), or 8/6.. That is the same as 12/9 above.
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