Question

In designing an experiment involving a treatment applied to 9 test​ subjects, researchers plan to use a simple random sample of 9 subjects selected from a pool of 27 available subjects.​ (Recall that with a simple random​ sample, all samples of the same size have the same chance of being​ selected.) Answer the questions below. a. How many different simple random samples are​ possible?

Answer 1

4686825

Explanation:

Given : Researchers plan to use a simple random sample of 9 subjects selected from a pool of 27 available subjects.​

To Find : How many different simple random samples are​ possible?

Solution:

Total subjects = 27

No. of subjects should be in sample = 9

So, to find How many different simple random samples are​ possible?

So, we will use combination

`^nC_r=(n!)/(r!(n-r)!)`

n = 27

r = 9

Substitute the values

`^(27)C_9=(27!)/(9!(27-9)!)`

`^(27)C_9=(27!)/(9!(18)!)`

`^(27)C_9=4686825`

Hence 4686825 different simple random samples are​ possible