Interpreting a survey result honestly
A school surveys 200 students about whether they would support a later start to the school day. Students are asked during a single lunchtime in the canteen, and 120 respond. Of those, 78 say yes. A newsletter article reports: '65% of students want a later start - a clear majority.' A separate count shows the school has 640 students in total. The survey organisers note that students who eat in the canteen may differ from those who do not, and that the response rate was low.
1. Calculate the percentage of respondents who said yes, and the percentage of the whole school population this represents. Comment on the newsletter's claim.
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Respondents saying yes: 78 out of 120 = 78 ÷ 120 = 65% - so the newsletter's arithmetic matches the respondents.\n\nBut as a share of the whole school: 78 ÷ 640 ≈ 12.2%.\n\nThe claim '65% of students' is misleading: it is 65% of those who happened to be in the canteen and chose to respond, not 65% of all 640 students. The 120 respondents are only 120 ÷ 640 = 18.75% of the school. The newsletter should say '65% of the 120 students who responded'.
2. Identify two sources of bias or error in this survey and explain how each could distort the result.
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1. Sampling bias (canteen location): Students who use the canteen may not represent the whole school - for example, they may be younger, or have different schedules or preferences. If canteen users are more likely to want a later start, the 65% overstates support.\n\n2. Non-response bias: Only 120 of 640 students (18.75%) responded. Students who feel strongly, or who have a free lunchtime, are more likely to answer. The views of the 520 who did not respond are unknown and could differ substantially.\n\nA fairer approach would be a random sample across year levels and times of day, with follow-up for non-respondents, and reporting the margin of uncertainty rather than a single headline figure.