Common Core: S-IC.5
Problem 42 of 45s12-042
In an experiment, fertilized seedlings grew 2 cm more on average than controls. Of 100 label re-shuffles, the gap was 2 cm in 2, 2.5 cm in 1, 3 cm in 1, never more. Significant at 5%?
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Solution walkthrough1:58
- Suppose the fertilizer does nothing. Then each seedling grows the same in either group, and only the split made the gap.
- Re-shuffle the labels at random and recompute the gap, 100 times. Each dot is one shuffle, placed at its gap.
- Mark the real gap, 2 cm. Shuffled gaps pile up around 0, as they should when the fertilizer does nothing.
- Count shuffles at least as large as the real gap: of , or .
- is below the cutoff: chance alone rarely gives a 2 cm gap, so the result is statistically significant.
- Traps: rare is not never; count 2 cm or more, not exactly 2 cm; and significant is evidence, not proof.