Question

An F₁ result gives you 80 brown and 40 white offspring. You suspect a dominant-recessive pair of alleles and a 3:1 ratio. Justify this hypothesis with the method of support (test of goodness of fit).

I believe we are supposed to gather our support limit from our 1 degree of freedom using df + 2√2df as well as using S(H₀/H₁) = ∑[o ln(o/e)] and comparing the two? I am not sure though and would like some help. Thanks!

Answer 1

We have to test the hypothesis that

Null hypothesis- Ho : Pair of alleles are in 3: 1 ratio.

against

Alternative hypothesis- Ha : Pair of alleles are not in 3: 1 ratio.

We use chi-square goodness of fit test for testing null hypothesis

The value of chi-square test statistic is

Oi : observed frequency and Ei : Expected frequency k = number of classes = 2, d.f. = k-1 =1

N = total number of offspring = 120

E₁ = ( 3/4) *120 = 90 and E₂ = (1/4) *120 = 30

Offspring	Oi	Ei	( Oi-Ei)^2/Ei
Brown	80	90	1.1111
White	40	30	3.3333
Total	120	120	4.4444

Value of chi-square test statistic  

Consider Alpha : level of significance = 0.05

Critical value at 1 degrees of freedom

Since calculated value is greater than critical value ( 4.4444 > 3.8414), we reject the null hypothesis at 5% level of significance.

Conclusion : At 5% level of significance, there is sufficient evidence support to claim that pair of alleles are not in 3: 1 ratio.