Design and power an A/B on question mix

You need to test whether replacing the 10% 'other' verbal questions with more grammar questions improves productivity in a 15-minute, 19-question section. Design a rigorous randomized experiment. Specify: (a) Unit of analysis, randomization scheme, and whether you use parallel arms (between-subjects) or a crossover (within-subjects) with counterbalancing to control learning effects; (b) Primary metric (e.g., correct answers per minute) and at least two guardrail metrics (e.g., fairness across native/non-native speakers, speed–accuracy trade-off); (c) Inclusion/exclusion criteria, pre-registration, blinding, and quality controls (e.g., proctoring, minimum reading times); (d) A sample-size calculation for detecting a +0.4 correct/attempt improvement with SD=2.8 at alpha=0.05 and 80% power using a two-sample t-test—show the formula and the final per-arm n; (e) Your stopping rule, multiple-comparisons plan (e.g., Holm–Bonferroni across subtypes), and how you will interpret effects if time-on-question changes but accuracy does not.