Reducing Error in a School Survey
A student council surveys 200 students about whether the canteen should open earlier. They stand at the main gate from 8:00 to 8:30 am and ask everyone who walks past. Of 200 responses, 68% say yes. The council concludes most students support the change and plans to submit the result to the principal. A teacher points out that students who arrive early may care more about opening times, and that students who arrive by bus or later may be missed. The council wants to know how reliable the 68% is and how to improve the survey without doubling their workload.
1. Identify the sampling method used and explain two sources of bias.
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Method: this is a convenience sample (whoever passes the gate during a fixed half-hour window). It is not a random sample, so results cannot be safely generalised to all students.
Bias source 1 - timing/self-selection: students arriving between 8:00 and 8:30 are more likely to be early arrivers, and early arrivers are precisely those most affected by canteen opening times. Their views on "open earlier" are systematically more positive than late arrivers'. This inflates the yes proportion.
Bias source 2 - coverage: students who arrive by bus, are dropped off later, or enter by another gate are under-represented or excluded. If those groups differ in their morning routines, the sample misses their opinions.
Because both biases push in the same direction (toward "yes"), the 68% is likely an overestimate of true support. The direction of bias matters more than its size: the council cannot claim 68% represents all students.
2. Propose a better sampling method the council could run in the same time, and justify it.
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Proposed method - stratified random sample by year group.
- Obtain the enrolment list with year levels.
- Choose a target sample size, e.g. 200 (same as before).
- Allocate proportionally: if Year 10 is 25% of the school, survey 50 of them, and so on.
- Within each year group, select students randomly (e.g. random numbers from the roll) and survey them at a neutral time and place, such as during form class or lunch, not at the gate.
Justification:
- Random selection removes self-selection - early arrivers no longer dominate.
- Stratifying by year ensures every year group is represented in proportion, fixing the coverage problem.
- Surveying at a neutral time reaches bus students and late arrivers.
This is feasible in the same effort because the council still surveys about 200 students; the change is who and where, not how many. If a full random draw is impractical, a quota approach (fixed numbers per year group, approached at lunch) is a reasonable compromise, though it is weaker than true random selection.
3. Explain how the council should report the result and what claim they can and cannot make.
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What they can claim: among the 200 students surveyed at the gate, 68% supported earlier opening. That is a factual statement about the sample.
What they cannot claim: that "most students" or "68% of the school" support the change. The convenience sample is biased toward early arrivers, so it cannot support a population claim.
Reporting guidance:
- State the method (who, where, when) so readers can judge bias.
- Report the sample size (n = 200).
- Report the figure as a sample result, not a school-wide estimate.
- Acknowledge the likely bias: "students arriving early may be over-represented."
If they rerun with the stratified random sample, they can then report a school-wide estimate with an indicative margin of error (roughly ±7 percentage points for n = 200 at 95% confidence, though the exact figure depends on the design). The judgement here is that a precise-looking 68% from a biased sample is less trustworthy than a stated, method-aware result - the council should not let the tidy number outrun the evidence behind it.