Answer to Question #214649 in Statistics and Probability for Hira

Question

Given the population 2, 4, 8, 8, 10, 10. Draw a sample of size n=2 without replacement and compute the sampling distribution of the mean.

Answer 1

There are six numbers. Possible samples of sizes 2 without replacement is ${6\choose 2}=15$

Note that 8 and 10 appear twice and are treated as unique numbers. The samples are

$(2,4),(2,8),(2,8),(2,10),(2,10),(4,8),(4,8),(4,10),(4,10), (8,8),(8,10),(8,10),(8,10),(8,10),(10,10)$

The order of the numbers does not matter since the interest is the elements of the samples.

The table below gives the means of the samples.

The sampling distribution of the mean is shown in the table below.