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6 exam-style questions with model answers, plus 8 quick multi-choice questions — every question on the site for this standard, grouped by the 2 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.
Write a comparison investigative question for an investigation comparing the median resting heart rate of students who play a sport with those who do not, using a given data set of New Zealand students. Explain why your wording is appropriate.
Two samples of 30 have medians of 42 and 47 minutes, with IQRs of 18 and 20 minutes and heavily overlapping box plots. A student writes: 'The median for group B is higher, so group B takes longer.' Explain what is wrong with this and rewrite it.
A student comparing weekly income between two occupation groups notes that both sample distributions are strongly right-skewed with several high outliers, but proceeds to compare means because 'the mean uses all the data'. Discuss.
A bootstrap 95% confidence interval for the difference in population medians (Group A − Group B) is 2.4 to 7.9 units. State whether a call can be made and what it is.
A student's bootstrap confidence interval for the difference in median commute times (city A − city B) is −1.8 to 6.3 minutes. She writes: 'The interval contains zero, so there is no difference in commute times between the two cities.' Explain what is wrong and rewrite the inference.
A student compares median household internet speed between two regions using samples of 800 from each. The bootstrap confidence interval for the difference is 0.4 to 1.1 Mbps, and she concludes that one region has significantly better internet and that investment should be directed to the other region. Discuss.