Problem Set 7
2. For the data set below, determine whether the genotype frequencies represent a population in Hardy-Weinberg Equilibrium. Use a x² test and show your work. Assume that this data allows you to imagine a perfectly representative sample of 1000 individuals. (The critical value at probability 0.05 with one degree of freedom is 3.84).
a. Sickle-cell hemoglobin: AA, 51.4 percent; AS, 47.6 percent; SS, 1.0 percent
AA = 0.514 * 1000 = 514
AS = 0.476 * 1000 = 476
SS = 0.01 * 1000 = 10
Frequency of A = p² + 0.5(2pq) = 0.514 + 0.5(0.476) = 0.752
Frequency of S = 1 - 0.752 = 0.248
Frequency of AA = p² * 1000 = (0.752)² * 1000 = 565
Frequency of AS = 2pq * 1000 = 2 * (0.752)(0.248) * 1000 = 373
Frequency of SS = q² * 1000 = (0.248)² * 1000 = 62
x² = Σ((observed - expected)² / expected)
x² = (514 - 565)² / 565 + (476 - 373)² / 373 + (10 - 62)² / 62 = 76.66
76.66
• The chi-square value is widely deviated from the Hardy Weinberg equilibrium since its nowhere near the critical value of 3.84