Question

suppose we have a populationof size N=5 consisting of the abe:6,8,10,12,and 14. take sample of size 2 with out replecment and construct sampling distribution of the sample mean.

Answer 1

Answer on Question #45168 – Math - Statistics and Probability

Suppose we have a population of size $N=5$ consisting of the above: 6,8,10,12,and 14. Take sample of size 2 without replacement and construct sampling distribution of the sample mean.

Solution

List all possible samples of size 2 that can be taken without replacement from this finite population:

{6,8}, {6,10}, {6,12}, {6,14}, {8,10}, {8,12}, {8,14}, {10,12}, {10,14}, {12,14}.

The mean of each sample in the same order as our list is

7, 8, 9, 10, 9, 10, 11, 11, 12, 13.

These are the 10 possible values of the random variable $\bar{X}$ each occurring with equal probability $\frac{1}{10}$.

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