A plant geneticist has two pure lines one with purple flower

A plant geneticist has two pure lines, one with purple flowers and one with blue. She hypothesizes that phenotypic difference is due to two alleles of one gene. To test this idea, she aims to look for a 3:1 ratio in the F2. She crosses the line and finds that all the F1 progeny are purple. The F1 plants are crossed and 400 F2 plants are obtained. Of these, 320 are purple and 80 are blue. Use the chi-square test to determine if these results fit hypothesis. What is the chi-square value (to two decimal points)?

Solution

Null hypothesis: Ho: The given flower species obey Mendelian laws.

Alternate hypothesis: The given species does not obey Mendelian laws.

F1 cross is Purple (PP) X Blue (pp)

Result = Purple (Pp)

F2 cross is Pp X Pp

Observed

Expected

(O-E)^2

(O-E)^2/E= chi square value

Purple

320

300

20

400

1.333333

blue

80

100

-20

400

4

5.333333

Calculated value = 5.33

Degree of freedom = (rows-1) (columns-1) = (5-1)* (2-1) = 4

Tabulated value = taken from chi square table = 9.49

Level of significance (assumed) = 0.05

Null hypothesis is accepted if calculated value is less than tabulated value.

Here, tabulated value>calculated value, so, null hypothesis should be accepted.

So, the flower color pattern is obeying Mendelian laws.

	Observed	Expected	(O-E)^2	(O-E)^2/E= chi square value
Purple	320	300	20	400	1.333333
blue	80	100	-20	400	4
					5.333333