2019 H2 Mathematics Paper 2 Question 6

Sampling Theory
Permutations and Combinations (P&C)

Answers

(i)

These 22 clubs form a population as she is only interested in Division One clubs and the 22 form the entire group she is interested in.

(ii)

He should get send a questionnaire to a sample of clubs.
For example, to get a sample of size 50, he can randomly select (using a random number generator) 11 clubs from Division One, 12 in Division Two, 13 in Division Three and 14 in Division Four.
Using a random number generator ensures that the sample he obtains is random and free from bias.
By sampling clubs proportional to the size of each division, the sample is representative of the population.

(iii)

7.24×1018{7.24 \times 10^{18}}

Full solutions

(i)

These 22 clubs form a population as she is only interested in Division One clubs and the 22 form the entire group she is interested in.

(ii)

He should get send a questionnaire to a sample of clubs.
For example, to get a sample of size 50, he can randomly select (using a random number generator) 11 clubs from Division One, 12 in Division Two, 13 in Division Three and 14 in Division Four.
Using a random number generator ensures that the sample he obtains is random and free from bias.
By sampling clubs proportional to the size of each division, the sample is representative of the population.

(iii)

Number of different samples
=(225)×(245)×(265)×(285)=7.24×1018  ■\begin{align*} & = {22 \choose 5} \times {24 \choose 5} \times {26 \choose 5} \times {28 \choose 5} \\ & = 7.24 \times 10^{18} \; \blacksquare \end{align*}