Question

The Frizzle fowl is a variety of chicken with “frizzled” (curly) feathers. In a 1930 experiment, Launder & Dunn crossed Frizzle fowls with a Leghorn variety that had straight feathers. The first generation of chicks all had slightly frizzled feathers. When the first generation was interbred, their offspring (the second generation) included 23 chicks with frizzled feathers, 50 with slightly frizzled feathers, and 20 with straight feathers. Under the most likely genetic model for this experiment, we would expect these phenotypes (i.e., feather types in this case) to occur in the ratios 1:2:1. Use a χ 2 goodness-of-fit test to determine whether the model is consistent with what was observed in the experiment. If you find that it isn’t consistent with observation, describe a more appropriate model.

Answer 1

Here chi square test for gooness of fit will be used. Hypotheses are:

H0: The data support the given inheritance model.

Ha: The data does not support the given inheritance model.

Following table shows the expected frequencies and calculations for chi square test statistics:

	O	E	(O-E)^2	(O-E)^2/E
	23	93/4=23.25	0.0625	0.002688172
	50	93/2=46.5	12.25	0.26344086
	20	93/4=23.25	10.5625	0.454301075
Total	93	96		0.720430108

So

2 = 0.7204

Degree of freedom:

df=n-1=3-1=2

So p-value of the test is 0.6975. Since p-value is greater than 0.10 so we fail to reject the null hypothesis. That is on the basis of sample evidence we can conclude that the data support the given inheritance model.