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Evaluating Statistical Reports · Part 3 of 5
9 exam-style questions with model answers, plus 12 quick multi-choice questions — every question on this part of the standard, grouped by the 3 pages of notes they come from.
Write a full answer before you reveal the model one. That comparison is where the learning happens.
A random sample of 400 people finds 38% support a proposal. Calculate the approximate margin of error and write down the confidence interval.
A report on a survey of 1 000 people states: 'Our margin of error is 3.2%, so our results are accurate to within 3.2%.' Explain why this statement is misleading.
A district council of 48 000 residents surveys 900 randomly selected residents and reports 61% satisfaction with its services, margin of error 3.3%. A councillor objects: 'Nine hundred people out of forty-eight thousand is under 2% of residents — far too small a sample to tell us anything.' Assess the councillor's objection and the survey's reliability.
A poll of 1 600 people finds 46% prefer option X and 41% prefer option Y. Calculate the margin of error for the difference and state whether the call can be made.
A survey of 900 people reports that 58% of the 250 respondents living in rural areas support a proposal, compared with 49% of the 650 urban respondents. The report concludes 'rural residents are more supportive'. Evaluate this claim.
A poll of 1 000 decided voters shows Party A on 36% and Party B on 33%, with Party A up 2 points and Party B down 1 point since last month's poll of 1 000 by the same company. The headline reads: 'Party A pulls ahead as Party B slides.' Assess the headline.
A study reports that a training course improved test scores by an average of 6 marks (95% CI: 2 to 10 marks). State what this interval tells you.
A newspaper reports: 'Taking the supplement halves your risk of the condition.' The underlying study found the risk fell from 6 in 100 000 to 3 in 100 000. Explain why the headline is misleading.
A report on a national road safety campaign states: 'In the 12 months after the campaign launched, road deaths fell by 8% compared with the previous 12 months. This statistically significant reduction demonstrates the campaign's effectiveness, and we recommend continued funding.' Assess this report with respect to its conclusion.