Question

Given: Population (6,7,8,9 and 10)

A sample of size 2 is to be Taken from this population.

a. How many samples are possible?

b. Construct sampling distribution of the sample means

Answer 1

There are $C_{5}^{2}=10$ possible samples.

The samples are

$\left( 6,7 \right) ,\bar{x}=6.5\\\left( 6,8 \right) ,\bar{x}=7\\\left( 6,9 \right) ,\bar{x}=7.5\\\left( 6,10 \right) ,\bar{x}=8\\\left( 7,8 \right) ,\bar{x}=7.5\\\left( 7,9 \right) ,\bar{x}=8\\\left( 7,10 \right) ,\bar{x}=8.5\\\left( 8,9 \right) ,\bar{x}=8.5\\\left( 8,10 \right) ,\bar{x}=9\\\left( 9,10 \right) ,\bar{x}=9.5\\\\P\left( \bar{x}=6.5 \right) =0.1\\P\left( \bar{x}=7 \right) =0.1\\P\left( \bar{x}=7.5 \right) =0.2\\P\left( \bar{x}=8 \right) =0.2\\P\left( \bar{x}=8.5 \right) =0.2\\P\left( \bar{x}=9 \right) =0.1\\P\left( \bar{x}=9.5 \right) =0.1$