Question

Arguably, the top 5 race horses in U.S. history are Secretariat (S), Man O'War (M), Citation (C), War Admiral (W), and Seabiscuit (B).

Required:
a. Use this information to determine the number of possible samples (without replacement) of size 22 that can be obtained from the population of size 55.
b. If a simple random sampling procedure is to be employed, the chances that any particular sample will be the one selected are:________

Answer 1

a) 10

b) 0.1 = 10%

Explanation:

The combinations formula is used to solve this question, since the horses are chosen without replacement.

Combinations formula:

`C_(n,x)` is the number of different combinations of x objects from a set of n elements, given by the following formula.

`C_(n,x) = (n!)/(x!(n-x)!)`

a. Use this information to determine the number of possible samples (without replacement) of size 2 that can be obtained from the population of size 5.

Combinations of 2 objects from a set of 5. So

`C_(5,2) = (5!)/(2!(5-2)!) = 10`

b. If a simple random sampling procedure is to be employed, the chances that any particular sample will be the one selected are:________

In this procedure, the samples are all equally as likely to be chosen.

So

1/10 = 0.1 = 10%