Question

Ok, so I'm struggling a bit with my labs being online due to covid. I was provided this information and an empty table.

"Sorghum is a genus of grass containing 25 species. Several species are grown in cultivation as livestock feed and one, Sorghum bicolor, is grown widely as a grain for human consumption and also for production of molasses and ethanol. It is one of the top five grain crops grown and consumed worldwide (along with wheat, corn, rice, and barley). Stem color is a character in Sorghum plants with two traits: red stems (dominant) or green stems (recessive). Complete Procedure 10.5 using the following data: 267 red stems and 103 green stems."

I believe I was meant to hypothesize the expected? Or was there a different way to attain that information through what was provided? Part B of the question is to state whether the hypothesis is supported or rejected, and show the rationale for my decision. Any help/explantation would be greatly appreciated! I have a handful more of these on my homework and I'd like to know that I'm doing them properly. Thank you =)

DATA BELOW

outcome	observed	expected	O-E	(O-E)2	(O-E)2/E
red	267	200	67	4489	22.45
green	103	87	16	256	2.94
total	370	287	83	x2calc=	24

Answer 1

Answer-

According to the given question-

We know that the Sorghum belongs to the genus of grass and having about 25 species, and these species are cultivated for livestock feed but the Sorghum bicolor, is grown for grain that is used for human consumption, for molasses production, as well as for ethanol production.

Here the color of the stem is chosen as a characteristic for the study, where the red color stem is dominant over the green color stem. in F2 generation we get following-

red stems = 267

green stems = 103

Total number of plants = 267 + 103 = 370

Suppose the Dominant allele (Red color) = R

Recessive allele (Green color) = r

Then genotype of Red plant = RR, and genotype of green plant = rr

When we make a cross between the true breeding line such as pure red plant with the pure green plant we get following offspring in the F1 generation.

RR rr

	r	r
R	Rr (Red stem plant)	Rr (Red stem plant)
R	Rr (Red stem plant)	Rr (Red stem plant)

So in the F1 generation, we get all offspring having a red color with genotype is Rr.

When we make a self cross between the offspring of F1 generation we get following offspring.

Cross between Rr Rr

	R	r
R	RR (Red stem plant)	Rr (Red stem plant)
r	Rr (Red stem plant)	rr  (Green stem plant)

In F2 generation we get both Red and green stem plant with a ratio of 3: 1

So the Expected frequency will be -

Red stem plant = 3 / 4 370 = 277.5

Green stem plant = 1 / 4 370 = 92.5

Chi-square characteristics-

	Observed frequency (O)	Expected frequency (E)	O -E	(O - E)2	(O - E)2 / E
Red stem plant	267	277.5	267 - 277.5 = - 10.5	110.25	110.25 / 277.5 = 0.397
Green stem plant	103	92.5	103 - 92.5 = 10.5	110.25	110.25 / 92.5 = 1.191
	Total = 370	Total = 370			X2 = 0.397 + 1.191 = 1.588

X² = 1.588

Degree of freedom = 2-1 = 1

The valve of Critical chi-square characteristics for 1 degree of freedom at the probability of 0.05 is 3.84

So the calculated valve of X² characteristics is less than the Critical value of chi-square i.e. X²   characteristics < X² Critical or 1.588 < 3.84 then we accept the null hypothesis.