Question

This problem has two parts:

Part 1.

In one of Mendel’s dihybrid crosses, he observed 315 round, yellow, 108 round, green, 101 wrinkled, yellow, and 32 wrinkled, green F2s. Analyze these data using the χ²test to see if they fit: (a) a 9:3:3:1 ratio and (b) the round: wrinkled data fit a 3:1 ratio. Show all of your work.

Part 2.

For both (a) and (b) of the problem above, what does the calculated p-value mean (i.e. what is the probability the difference between your expected and observed data  is due to chance)?

Answer 1

Answer:

Part1:

a).

Then, let us try whether they fit in 9:3:3:1 ration…

Dihybrid F2 phenotypic ratio = 9:3:3:1

Total progeny = 315+108+101+32 = 556

Round, yellow = 9/16* 556

Round, green = 3/16*556

Wrinkled, yellow = 3/16*556

Wrinkled, green = 1/16*556

Phenotype	Observed(O)	Expected (E)	O-E	(O-E)2	(O-E)2/E
round, yellow	315	312.750	2.25	5.06	0.0162
round, green	108	104.250	3.75	14.06	0.1349
wrinkled, yellow	101	104.250	-3.25	10.56	0.1013
wrinkled, green	32	34.750	-2.75	7.56	0.2176
Total	556	556			0.4700

X^2 value = 0.47

Degrees of freedom = Number of phenotypes – 1

Df = 4-1=3

P value = 7.815

The chi-square value of 0.47 is less than the critical value of 7.815. We can accept the null hypothesis and the data is fit in 9:3:3:1.

b). The data doesn’t fit in to the 3:1 ratio as 4 types of traits are found.

Part 2:

a).

Degrees of freedom = Number of phenotypes – 1

Df = 4-1=3

P value = 7.815 (stadard value)

b). Degrees of freedom = Number of phenotypes – 1

Df = 2-1=1

P value = 3.84 (stadard value)