S1. Populations, samples and random statistics

Question 1

Define population

Answer 1

Either as:

• A complete enumeration of some set of interest
• A mathematical model which generates a set of interest

Question 2

Define sample

Answer 2

A subset of a population of interest.

Question 3

Define sampling

Answer 3

The process of selection of a subset of individuals from a population to form a sample.

Question 4

Define sampling frame

Answer 4

The source material or device from which a sample is drawn.

Question 5

What is Simple Random Sampling (SRS)?

Answer 5

Sampling which selects pre-determined number of respondents from a population with each having an equal non-zero chance of selection.

Question 6

What is meant by a representative

Answer 6

If it was repeated many times it would display features of the population which remain relatively the same.

Question 7

What is quota sampling?

Answer 7

Selection which specifies fixed quotas of certain types of respondents such that the resulting sample is representative.

Question 8

Issues with quota sampling

Answer 8

• While is may be representative of observed characteristics, it may not be representative of unobserved characteristics.
• Used before probability sampling, which removes sample selection bias.

Question 9

What are random variables?

Answer 9

Generated using random sampling

Not technically random and not variables. They are deterministic function which assign numbers to uncertain events.

Question 10

What is meant by ‘iid’ variables?

Answer 10

Independently and Identically Distributed variables.

Where each sample has an equal and independent chance of being selected (achieved easily by replacement) and the PMF is the same for all sample values.

Question 11

Implication of iid variables

Answer 11

By having the same distribution as the population, they also have the same expected values and other moments as the population.