Answer to Question #295470 in Statistics and Probability for Jen

Question

Consider a population consisting of a 2,3,4,5,6.Suppose sample size of 2 are drawn from this population. Describe the sampling distribution of the sanple means.

Answer 1

We define the population size (N) = 5

Sample size (n) = 2

So the number of possible samples = (5C2) = 10 possible samples.

Thus all the possible samples are:

( (2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6) )

The sample means are as below:

(2+3)/2 =2.5

(2+4)/2 =3

(2+5)/2 =3.5

(2+6)/2 =4

(3+4)/2 = 3.5

(3+5)/2 =4

(3+6)/2 =4.5

(4+5)/2 =4.5

(4+6)/2 = 5.0

(5+6)/2 = 5.5

Hence the overall sample mean of the sampling distribution is given as below

1/10 (2.5 +3+3.5+4+3.5+4+4.5+4.5+5+5.5) = 4

which is the sample mean.

Variance of the sampling distribution is obtained as below

(1/10 (2.5² +3² +3.5² +4² +3.5² + 4² +4.5² + 4.5² + 5² + 5.5²) ) - ( 4² ) which results to 0.75

Mean of the population = (2+3+4+5+6)/5 = 4

Mean of population = sample mean = 4