Question

Geneticists examined the distribution of seed coat color in cultivated amaranth grains, Amaranthus caudatus. Crossing black-seeded and pale-seeded A. caudatus populations gave the following counts of black, brown, and pale seeds in the second generation.

Seed Coat Color	black	brown	pale
Seed Count	327	79	28

According to genetics laws, dominant epistasis should lead to 12/16  of all such seeds being black,  3/16  brown, and  1/16  pale. We want to test this theory at the 1% significance level.

(a)	Find the value of the test statistic.

(b)	Fiind the critical value.

(c)What is the conclusion?

(A) We conclude that the data is consistent with the theory since the answer in (a) is greater than the answer in (b). (B) We conclude that the observed frequencies contradict the theory since the answer in (a) is bigger than the answer in (b). (C) We cannot conclude that the observed frequencies contradict the theory since the answer is (a) is greater than the answer in (b). (D) We conclude that the theory is true since the answer in (a) is less than or equal to the answer in (b). (E) We cannot conclude that the observed frequencies contradict the theory since the answer in (a) is less than or equal to the answer in (b). (F) We conclude that the theory is true since the answer in (a) is greater than the answer in (b). (G) We conclude that the observed frequencies contradict the theory since the answer in (a) is less than or equal to the answer in (b).

Answer 1

a)

applying chi square goodness of fit test:

	relative	observed	Expected	residual	Chi square	likelihood ratio
category	frequency(p)	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei	G2 =2*Oi*ln(Oi/Ei)
0	0.75	327.0	325.50	0.08	0.007	3.0069
1	0.19	79.0	81.38	-0.26	0.069	-4.6800
2	0.06	28.0	27.13	0.17	0.028	1.7779
total	1.000	434	434		0.1045	0.1048
test statistic X2 =	0.104

b)

for 0.01 level and 2 df :crtiical value X2 =

9.2103

c)

(E) We cannot conclude that the observed frequencies contradict the theory

since the answer in (a) is less than or equal to the answer in (b).