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36 exam-style questions with model answers, plus 48 quick multi-choice questions — every question on the site for this standard, grouped by the 12 pages of notes they come from.
Write a full answer before you reveal the model one — that comparison is where the marks come from. Every block links back to the notes that teach it.
Name the five stages of the statistical enquiry cycle, and state which stage a poor choice of sampling method belongs to.
A supermarket chain reports: 'We surveyed 600 shoppers as they left our Auckland stores on a Saturday. 82% rated our fresh produce as good or excellent, so New Zealand shoppers are happy with our produce.' Identify one weakness in the Plan stage and justify what it means for the conclusion.
A health charity reports: 'We invited members of our online support community to complete a wellbeing questionnaire. 3 400 of 11 000 members responded (31%). Respondents who used our counselling service scored on average 8 points higher on the wellbeing scale than those who did not. Our counselling service improves wellbeing.' Evaluate the quality of this report with respect to its conclusion.
Explain the difference between a parameter and a statistic, giving an example of each.
A polling company states: 'Our sample of 12 000 people, recruited through advertisements on our news website, is so large that the results are highly accurate.' Explain why the large sample size does not justify this claim.
A council surveys transport habits by stopping people in the central city between 7am and 9am on weekdays and asking how they travelled in. It reports: '46% of people arriving in the central city travel by car. Congestion is therefore less severe than commonly believed, and the planned parking expansion is unnecessary.' Assess the quality of this report with respect to its conclusion.
Describe stratified sampling and give one reason a researcher might choose it over simple random sampling.
A magazine prints a questionnaire and invites readers to post it back. 4 200 replies are received and the magazine reports that '78% of readers are dissatisfied with their broadband provider'. Explain why this figure is likely to overstate dissatisfaction, referring to the sampling process.
A market research firm reports: 'We recruited 1 500 respondents from our online panel and weighted results by age, gender and region so the sample matches the New Zealand population. Our margin of error is 2.5%. 61% of New Zealanders say they would pay more for locally produced food.' Assess this methodology with respect to the conclusion drawn.
Explain the difference between undercoverage and non-response bias, with an example of each.
A council survey asks: 'Do you support the council's plan to protect our parks by increasing rates by 2%?' 68% said yes. Explain two problems with this question and what each means for the 68% figure.
A government agency reports: 'A face-to-face survey of 2 000 randomly selected adults found that 12% reported drinking more than the recommended weekly alcohol limit, down from 18% in the previous survey, which was conducted online. Hazardous drinking has fallen sharply.' Assess this report with respect to its conclusion.
A poll of 1 000 voters has a maximum margin of error of about 3.1%. A party's support moves from 24% to 26%. What can be concluded?
A poll reports party percentages after excluding the 16% of respondents who were undecided. Explain what this means for how the published figures should be interpreted, and one risk it creates.
Two polls are published in the same week. Company A (n = 1 000, phone) has Party X on 34%; Company B (n = 1 200, online panel) has Party X on 29%. A commentator writes: 'The polls disagree, so at least one of them must be wrong.' Assess this statement.
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.
Explain the difference between random selection and random allocation, and state what each allows a study to claim.
A study finds that children who attend early childhood education score higher in literacy at age 8. The report concludes that early childhood education raises literacy. Explain why the design does not support this, and describe a study that would.
A company reports: 'We offered all 1 200 staff an optional four-day working week. The 380 who took it up recorded 11% higher productivity over the following six months than those who stayed on five days. The four-day week raises productivity, and we recommend it industry-wide.' Assess this report with respect to its conclusion.
Define a confounding variable and give an example for the observed association between the number of firefighters at a fire and the amount of damage caused.
A study reports that people who eat breakfast weigh less than those who skip it, and concludes that eating breakfast prevents weight gain. Give two alternative explanations for the association and explain each.
A regional health board reports: 'Since our free flu vaccination programme began in the 20 suburbs with the highest hospital admission rates, admissions in those suburbs have fallen by 14%, while admissions across the rest of the region rose 2%. The programme is working and should be extended region-wide.' Assess the causal claim.
A bar chart comparing four values (81, 83, 84, 87) uses a vertical axis starting at 80. Explain the effect this has on the reader.
A report states: 'Auckland recorded 4 200 burglaries last year, compared with 380 in Nelson. Auckland is more than ten times as dangerous.' Auckland's population is about 1 700 000 and Nelson's about 55 000. Evaluate the claim.
A property website reports: 'The average house price in our region rose from $780 000 to $845 000 this year, an increase of 8.3%. Our graph, with the vertical axis from $770 000 to $850 000, shows the dramatic climb. Now is the time to buy before prices rise further.' Assess this report.
State the three moves that make up a complete evaluative point, and what each contributes.
A report states: 'We interviewed 200 people at three shopping centres on a weekday afternoon. 64% said they would use a new express bus service. Demand is strong, so the service should be introduced.' Make one fully developed evaluative point.
A telecommunications company reports: 'An independent research firm surveyed 1 100 randomly selected New Zealanders. 46% named us as having the most reliable mobile network, compared with 38% for our nearest competitor. We have the most reliable network in New Zealand.' Evaluate this report.