Imagine that you have identified two new traits in pea plant

Imagine that you have identified two new traits in pea plants, and you wish to determine whether they behave according to Mendel\'s Law. You perform a di-hybrid cross and count the number of offspring in each phenotypic class.

a). In a small experiment you observe four distinct phentotypic classes with the following numbers of individuals in each class: 8:4:4:1. Calculating Chi-squared gives you a value of 0.625. Using a p = 0.05 cutoff, does the observed data agree with Mendel\'s Law?

b). In a follow-up experiment you observe the same four distinct phenotypic classes, which of the following number of individuals in each class: 80:40:43:7. Calculating Chi-squared gives you a value of 8.97. Using a p = 0.05 cutoff, does the observed data agree with Mendel\'s Law?

Solution

The Mendel\'s dihybrid cross deals with the Law of independent Assortment.

The phenotypic F2 ratio of dihybrid cross is 9:3:3:1.

a) in part a, the F2 ratio is 8:4:4:1, with chi-squared gives a value of 0.625 at p= 0.05. the observed data does not agree with the Mendal\'s law, because the calculated data (7.7) is greater than the critical value (0.625) at p=0.025.

i.e, the expected value of chi-squared is 0.77.

b) In part (b), the observed F2 ratio of dihybrid cross is 80:40:43:7.

But the approximate expected F2 ratio of this dihybrid cross will be 95:32:32:11.

The observed data does not agree with the Mendel\'s Law, because the calculated value (9.6) is greater than the critical value of 8.77.

Here the calculated value of the chi square test is 9.6.

It is important to note that the data does not fit to the model if the chi square calculated is greater than the critical value. on the other hand the data did fit to the model when the chi square calculted is less than the critical value.

Here, both the cases shows calculated value greated than the critical value and thus the data does not fit to the model,