SOLUTION: there are three values in a population ,(10,30,and 50) and we are interested in investigating the sampling distributtion of the sample mean (x par )for sample of size 2.

Question 1083823: there are three values in a population ,(10,30,and 50) and we are interested in investigating the sampling distributtion of the sample mean (x par )for sample of size 2. -How many possible distinct random sample are ther ? A ssumes sampling whit replacement . - find the mean and variance of this distribution -Assume sampling without replacement , how many possible random samples are there now ? what is sampling distribution now ?
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
there are 3! = 6 possible distinct random samples with replacement
:
(10,10), (10,30), (10,50), (30,30), (30,50), (50,50)
:
the population mean is (10+30+50) / 3 = 30 and variance = ( (10-30)^2 + (30-30)^2 + (50-30)^2 ) / 3 = 266.6667
:
now consider our samples
:
(10,10) - the mean is 10
(10,30) - the mean is 20
(10,50) - the mean is 30
(30,30) - the mean is 30
(30,50) - the mean is 40
(50,50) - the mean is 50
:
the mean of the sampling distribution is (10+20+30+30+40+50) / 6 = 30
the variance of the sampling distribution is 166.6667
:
there are 2 possible distinct random samples without replacement
:
(10,30), (30,50)
:
(10,30) - the mean is 20
(30,50) - the mean is 40
:
the mean of the sampling distribution is (20+40) / 2 = 30
the variance of the sampling distribution is 100
:

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