A-Level Sampling Practice Questions

Recall what a population means

In statistics the population is the whole group we are interested in, not just the people we measure. It is the complete set we want to draw conclusions about.

Identify the group in this study

The study is about the heights of the college students, so the group of interest is those students. That tells us what the population must be.

State the size and conclusion

There are 1200 students, and every one of them is part of the group being studied. So the population is all 1200 students.

Recall the aim of a sample

A good sample reflects the whole population fairly. We want the sample to be like a mini version of the population.

Describe what goes wrong when biased

A biased sample does not reflect the population fairly, so some outcomes appear too often or too rarely. This makes conclusions misleading.

State the definition

So a biased sample is one that does not fairly represent the population. That is the correct description.

Recall stratified sampling

Stratified sampling divides the population into groups and picks randomly within each. The random step is important.

Recall quota sampling

Quota sampling also uses group targets but the interviewer picks whoever is available. There is no random step.

Identify the shared feature

Both methods split the population into groups with targets. So the groups are not the difference.

Identify the difference

The real difference is how members are chosen within each group. Stratified is random; quota is not.

Note the consequence

Because quota selection is non-random, it can introduce interviewer bias. Stratified avoids this within strata.

Conclude

So in stratified sampling members are chosen randomly, while in quota sampling they are chosen non-randomly. That is the key difference.

Write the known values

We know the population, the sample size and this stratum's size. These give the answer.

Find the sampling fraction

The sampling fraction is the sample size over the population. This is the share taken from each stratum.

Simplify the fraction

Dividing 150 by 3000 gives 0.05, so we take 5% of each group. This keeps the sample proportional.

Apply to the stratum

We take 5% of the 640 members. Multiply 640 by 0.05.

Evaluate

This gives exactly 32. No rounding is needed.

Check reasonableness

32 out of 640 is 5%, matching the sampling fraction. So the answer is consistent.

Compare with population share

The stratum is about 21% of the population, and 32 is about 21% of 150. This cross-check agrees.

Confirm no rounding issue

Since 32 is already a whole number, there is nothing to round. The result stands.

Restate the calculation

So five percent of 640 is 32. This is the sample from the stratum.

State the answer

So 32 are sampled from this stratum. That is the required value.

State the requirements

The study is national, needs high representativeness across regions and ages, and has a full register plus a computer. The method must use these strengths.

List the candidate methods

The five standard methods are simple random, systematic, stratified, quota and opportunity. We assess each against the requirements.

Assess opportunity sampling

Opportunity sampling uses whoever is available and ignores regions and ages. So it fails the representativeness requirement.

Assess quota sampling

Quota sampling controls groups but selects non-randomly and does not use the register. It risks interviewer bias, so it is not ideal.

Assess simple random sampling

Simple random sampling uses the register fairly, but region and age balance is left to chance. Small regions could be under-represented.

Assess systematic sampling

Systematic sampling is easy on a computer but does not guarantee proportional regions and ages. It also risks periodicity in an ordered list.

Assess stratified sampling

Stratified sampling divides the register into region and age strata and samples each in proportion at random. This directly targets representativeness.

Use the register

The complete register lets us identify each person's region and age. So we can form the strata accurately.

Use the computer

A computer can quickly compute proportional shares and pick random members from each stratum. So the extra work of stratification is easy here.

Note the representativeness gain

Stratified sampling guarantees each region and age group appears in proportion. This is exactly what the study needs.

Note the randomness benefit

Selection within each stratum is random, so bias is minimised. This beats quota sampling's non-random choice.

Compare with simple random

Unlike simple random sampling, stratified sampling removes the risk of chance imbalance between groups. So it is more representative.

Weigh the trade-off

Stratified sampling needs known group sizes, and the register provides them. So the only drawback is covered.

Eliminate the weaker methods

Opportunity, quota, simple random and systematic each fail on representativeness or use of the register. So they are eliminated.

Select stratified sampling

Stratified random sampling meets every requirement using the register and computer. So it is the best method.

Conclude

So stratified random sampling is best: the computer allocates proportional random samples to each region and age stratum from the register, giving high representativeness. That is the correct choice.