The Debate Team's Practice Data
A debate team tracked practice outcomes over 8 weeks. In weeks 1–4, the team held 20 practice rounds and won 12. In weeks 5–8, after changing their opening strategy, they held 30 rounds and won 21. A coach claims the new strategy 'raised the win rate by 10 percentage points, so it clearly works.' A team captain notes that in weeks 5–8 the opponents were also stronger on average, and that two of the 30 rounds were against a team that forfeited halfway through. The team wants to decide whether to keep the new strategy for the regional tournament.
1. Compute the win rate for each period and check the coach's '10 percentage points' claim.
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Weeks 1–4: 12 ÷ 20 = 0.60 = 60%. Weeks 5–8: 21 ÷ 30 = 0.70 = 70%. The difference is 70% − 60% = 10 percentage points, so the coach's arithmetic is correct. But note the sample sizes differ (20 vs. 30 rounds) and are both small, so a 10-point gap could easily arise from chance; the claim is numerically accurate but the inference that the strategy 'clearly works' goes beyond the data.
2. The captain raises two complications: stronger opponents and two forfeited rounds. Explain how each could affect the comparison and why the conclusion is uncertain.
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Stronger opponents in weeks 5–8 would tend to lower the win rate, so if the rate rose anyway, that actually strengthens the case for the strategy-but it also means the two periods aren't comparable, so the 10-point gap isn't a clean measure of the strategy alone. The two forfeited rounds are more troubling: if they were counted as wins, the true competitive win total is 19 of 28 (about 67.9%), shrinking the gain to roughly 7.9 points; if counted as losses, it's 21 of 30 only if they were wins, so the accounting matters. Because the data mix a strategy change with opponent strength and ambiguous forfeit handling, the team cannot conclude the strategy 'clearly works.' Keeping it for the tournament is a reasonable but not proven choice, ideally tested with more rounds and consistent record-keeping.