Question

An F_{1} 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*√2*df as well as using
S(H_{0}/H_{1}) = ∑[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

E_{1} = ( 3/4) *120 = 90 and E_{2} = (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.

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