6 Consider the following population 2 2 4 5 Suppose that a r

6.   Consider the following \"population\": {2, 2, 4, 5}. Suppose that a random sample of size n = 2 is to be selected without replacement from this population. There are 6 possible samples (since the order of selection does not matter). Compute the sample mean for each of these samples and use that information to construct the sampling distribution of . (Display it in table form.)

Solution

Population Size N = 4, units 2,2,4,5 and sample size n = 2. The number of possible ways 4c₂ = 6.

Possible samples : (2,2)     (2,4)    (2,5)      (2,4)    (2,5)     (4,5)

Means                 :   2          3        3.5     3          3.5       4.5

Again the sampling distribution of mean is

Means                 : 2            3             3.5                4.5

Probabilities        : 1/6        2/6             2/6                1/6 Verify that sum of all probabilities is equal to 1

The above table is called \"Sampling distribution of Mean\".