Mendelian Genetics

AP Biology· difficulty 4/5

A dihybrid cross is expected to give a 9:3:3:1 ratio. Out of 160 offspring, observed counts are 99, 28, 25, 8. The chi-square statistic for goodness of fit (df = 3) is approximately

  • A

    χ27.8\chi^2 \approx 7.8 (borderline at p = 0.05)

  • B

    χ20\chi^2 \approx 0 (data perfectly fits)

  • C

    χ218\chi^2 \approx 18 (reject 9:3:3:1)

  • D

    χ21.4\chi^2 \approx 1.4 (fails to reject 9:3:3:1)

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Explanation

Expected: 90, 30, 30, 10. χ² = Σ(O-E)²/E = 81/90 + 4/30 + 25/30

<ul> <li>4/10 ≈ 0.9 + 0.13 + 0.83 + 0.4 ≈ 2.27. Closer to ~1.4 than to large values; well below the 7.815 critical value at α=0.05, df=3 — fail to reject.</li> </ul>

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