Geneticists examined the distribution of seed coat color in cultivated amaranth grains, Amaranthus caudatus. Crossing black-seeded...

Seed Coat Color	black	brown	pale
Seed Count	307	75	32

According to genetics laws, dominant epistasis should lead to

of all such seeds being black,

brown, and

pale. We want to test this theory at the 1% significance level.

(a)	[2 marks] Find the value of the test statistic.

(b)	[1 mark] Fiind the critical value.

(c)	[1 mark] What is the conclusion?

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

Solutions

Expert Solution

applying chi square goodness of fit test:

	relative	observed	Expected	residual	Chi square
category	frequency(p)	O_i	E_i=total*p	R²_i=(O_i-E_i)/√E_i	R²_i=(O_i-E_i)²/E_i
1	3/4	307	310.50	-0.20	0.039
2	3/16	75	77.63	-0.30	0.089
3	1/16	32	25.88	1.20	1.450
total	1.000	414	414		1.5781

test statistic X² =		1.5781

degree of freedom =categories-1=			2
for 0.01 level and 2 df :crtiical value X2 =				9.2103

(F) 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).

orchestra answered 2 years ago

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