Question

Hair type is an example of incomplete dominance (H^CH^C = Curly, H^CH^S = Wavy, H^SH^S = Straight).  A population contains 80 curly, 5 wavy, and 15 straight individuals.  Perform a chi-square analysis to determine whether or not this population is in Hardy-Weinberg equilibrium.

a) Calculate your expected values

b) Perform a chi-square analysis

Answer 1

Given:

Hair type is an example of incomplete dominance (HCHC = Curly, HCHS = Wavy, HSHS = Straight).  A population contains 80 curly, 5 wavy, and 15 straight individuals.

Hypothesis test:

The null and alternative hypothesis is

Ho : p1 = p2 = p3 = 1/3

Ha : At least one of population is not in Hardy-Weinberg equilibrium.

Table for calculating Chi square test statistic :

Expected frequency E = Total frequency/number of categories

Hair type	Observed frequency O	Expected frequency E	(O-E)2/E
Curly	80	100/3 = 33.33	65.3492
Wavy	5	100/3 = 33.33	24.0801
Straight	15	100/3 = 33.33	10.0807
Total	100	100	(O-E)2/E = 99.51

Test statistics:

2 = (O-E)2/E = 99.51

Degree of freedom, df = k-1 = 3-1 = 2

P-value:

P-value corresponding to Chi square test statistic 99.51 with degree of freedom , df = 2 is

P-value = 0.00001

Since P-value is less than significance level, = 0.05, we reject null hypothesis.

Conclusion : There is sufficient evidence to conclude that this population is in Hardy-Weinberg equilibrium.