This comprehensive quiz covers all 12 lessons of Statistical Analysis. It includes multiple choice questions drawn from the entire module pool, plus short answer questions that test your ability to apply statistical reasoning in unfamiliar contexts. Aim for 80% or higher to demonstrate mastery. Good luck!
15 questions drawn from all 12 lessons - feedback shown immediately
Short Answer
1. A city council is considering banning cars from the CBD to reduce pollution. They present data showing a correlation between car density and air quality index. (a) Explain why correlation alone is insufficient to justify the ban. (b) Identify at least three lurking variables that could explain the correlation. (c) Design a study that would provide stronger evidence for causation. (d) Discuss the difference between statistical significance and practical significance in this policy context. 4 MARKS
2. Two schools report their HSC results. School Alpha: mean=80, median=82, SD=8, n=150. School Beta: mean=78, median=75, SD=15, n=150. (a) Compare the distributions comprehensively. (b) A parent argues School Alpha is better because its mean is higher. A teacher argues School Beta is better because it has more high achievers (wider spread). Evaluate both arguments using statistical reasoning. (c) What additional information would help you make a fair comparison? (d) If you were choosing a school for a risk-averse student and a risk-tolerant student, which would you recommend and why? 4 MARKS
(a) A correlation is an association, not proof that changing car density caused the change in air quality. A third factor could affect both, or pollution could affect traffic patterns; the data alone do not establish which direction the effect runs.
(b) Possible lurking variables include weather and wind direction, industrial emissions, population density, construction activity, public transport access, and seasonal changes. Each could vary with car density and also affect measured air quality.
(c) A stronger study could compare the CBD before and after a staged car restriction with a similar area that does not introduce one. Measure traffic and the same air-quality indicators at both sites over the same dates, account for weather, season and industrial activity, and check whether the change is larger in the restricted area. A randomized phased rollout across comparable zones would reduce confounding further if practical.
(d) Statistical significance asks whether an observed difference is unlikely under a no-effect model; practical significance asks whether its size matters for health and policy. A small improvement can be statistically detectable with many observations yet too small to justify the cost or disruption. Consider the estimated effect, uncertainty, health impacts, costs and who benefits.
(a) Alpha's mean is 80 and median 82, compared with Beta's mean 78 and median 75. Alpha's scores are less spread out (SD 8 versus 15). The summaries suggest higher central results and greater consistency for Alpha. Mean below median for Alpha and mean above median for Beta may hint at different skew, but these summaries alone do not establish distribution shape.
(b) The parent is right that Alpha has the higher reported mean, but that alone does not prove the school is better. The teacher's claim that Beta has more high achievers does not follow from a larger SD: Beta may have more low scores as well, and the upper tail is unknown. Neither conclusion is established without the full score distributions and comparable student groups.
(c) A fairer comparison would include score distributions or percentiles, subject mix, prior attainment, cohort and admission differences, relevant demographic and resource context, and results over several years. Value-added progress and student wellbeing or post-school outcomes could also inform what “better” means.
(d) On these summaries alone, Alpha is the more defensible choice for a risk-averse student because it has a slightly higher centre and much lower variability. The data do not justify recommending Beta for a risk-tolerant student: a larger SD does not show that its extra variation is concentrated among high scores. More information about the upper tail and the student's goals is needed.
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