Question

Give Chi square, degrees of freedom, probability and accept/reject. Round all numbers to two decimals throughout. Make sure to show all your work:

In corn, purple kernels are dominant over yellow kernels, and full kernels are dominant over shrunken kernels.

A corn plant with purple, full kernels is crossed with a plant having purple, full kernels. The following progeny are obtained:

Purple, full                   100

Purple, shrunken          36

Yellow, full                   30

Yellow, shrunken          8

Determine the genotypes of the parents and progeny.

Test your hypothesis with a Chi square test until it is accepted.

Answer 1

Consider the purple kernel allele to be P and the yellow kernel allele be p. The full kernel allele is F and the shrunken kernel allele is f. Punnett square for the cross between purple full kernel and purple full kernels. Since yellow full and yellow shrunken phenotypes were observed, the parents in the cross are heterzygotes.

			Parent 1
			PpYy
			PY	Py	pY	py
Parent 2	PpYy	PY	PPYY Purple full	PPYy Purple full	PpYY Purple full	PpYy Purple full
		Py	PPYy Purple full	PPyy Purple Shrunken	PpYy Purple full	Ppyy Purple Shrunken
		pY	PpYY Purple full	PpYy Purple full	ppYY Yellow Full	ppYy Yellow Full
		py	PpYy Purple full	Ppyy Purple Shrunken	ppYy Yellow full	ppyy Yellow shrunken

Parental genotype= PpYy

Progeny Genotype: PPYY,PPYy,PpYY,PpYy, PPyy, Ppyy, ppYY, ppYy,ppyy

Phenotype ratio is 9 purple full: 3 purple shrunken: 3 Yellow Full: 1 Yellow shrunken (9:3:3:1)

Ch-Square test:

Calculation for Expected Number:

Null Hypothesis: There is no difference between the observed and expected values. The observed valves match the expected values of 9:3:3:1.

Total number of offspring= 174

174/ 16= 10.875=10.875

Purple Full= 9 X 10.875= 97.875=97.88

Purple Shrunken= 3 x 10.875= 32.625= 32.63

Yellow full= 3 X 10.875= 32.63

Yellow Shrunken= 10.88

	Observed (O)	Expected	O-E	(O-E)2	(O-E)2/E
Purple Full	100	97.88	2.12	4.49	0.05
Purple Shrunken	36	32.63	3.37	11.36	0.35
Yellow Full	30	32.63	-2.63	6.91	0.21
Yellow Shrunken	8	10.88	-2.88	8.29	0.76
Total	174	174	-0.02	31.05	1.37

Degree of Freedom= Total number of phenotypes-1= 4-1= 3

Probability from Chi Square table= 0.71= 0.71 X 100= 71%

A Chi Square value between 1%-5% should allow you to reject the null hypothesis. However, 71% is a large P Value. Hence, the null hypothesis is accepted. There is no significant difference between the expected and observed values.