S1 Statistical sampling — coverage pack
1 specification leaves · notes, questions, answers and worked methods
S1.1 · Understand and use the terms 'population' and 'sample'; use samples to make informal inferences about the population; use sampling techniques including simple random and opportunity sampling; select or critique techniques in context.
- The population is the complete set about which an inference is required; a sample is the subset from which data are actually collected.
- A simple random sample gives every member an equal selection chance; systematic sampling uses a fixed interval after a random start, while stratified sampling preserves chosen population proportions.
- Quota sampling fills category targets without random selection, whereas opportunity sampling uses whoever is available; both are quick but vulnerable to selection bias.
- When drawing an informal inference, discuss representativeness, sampling frame, non-response and sample size; a large biased sample is not automatically reliable.
Tier 1 · Easy
1. A college wants to estimate the weekly study time of all students. It records the study time of students. State the population and the sample.[2 marks]
Answer
- Population: all students at the college.
- Sample: the students whose study times were recorded.
Method: Identify the whole group about which the estimate is required: all students. The observed subset consists of the students, so that subset is the sample.
Tier 2 · Standard
1. A theatre has a numbered list of its members. Describe how to select a simple random sample of members.[3 marks]
Answer
- Label the members to .
- Use a random-number generator to obtain distinct integers from to .
- Select the members with those labels.
Method: Use the complete membership list as the sampling frame. Assign each member one unique number, generate numbers uniformly from the full range, and ignore repeats until different labels have been obtained. This gives each member an equal chance of selection.
Tier 3 · Hard
1. To estimate support for extending library opening hours, a researcher asks the first people entering the library after pm. Of these, support the proposal. Critique the sampling method and the inference that about of all town residents support the proposal.[5 marks]
Answer
- This is an opportunity sample.
- Late-evening library users are likely to be more supportive than residents who do not use the library then, so the sample is biased.
- The sampling frame excludes many town residents, and repeat/non-response details are unknown.
- Therefore the sample proportion should not be generalised to all town residents.
Method: The participants were chosen because they were available at one place and time, so the method is opportunity sampling. The selection mechanism over-represents people who already use the library late. Although the observed sample proportion is , its bias matters more than its size, so it does not justify the stated population inference. A simple random sample from a suitable register of residents would be more representative.