Chi-Squared Test for Pea Plant Crosses: Calculate, Interpret, and Analyze

[leah3000]

Homework Statement

In a cross between two types of pea plants, one heterozygous for the round yellow seed condition, and the other, pure breeding with wrinkled green seeds, the following offsprings were recorded;

Round yellow peas-- 108
Round green peas-- 102
Wrinkled yellow peas--105
Wrinkled green peas-- 101

Homework Equations

$$\chi$$ ^2 = $$\Sigma$$ {O-E)^2 / E}

The ratio of a heterozygous cross with a homozygous recessive

The Attempt at a Solution

I calculated the value of $$\chi$$ ^2 to be 0.28. The degrees of freedom= no. of categories-1 = 3.

I'm a little bit confused on how to relate the calculated value of $$\chi$$ ^2 to the probability value in the distribution table.

I took the probability value as > 0.1 and got 6.25 according to the data in the table. I'm now assuming that it isn't a significant deviation as the value of $$\chi$$ ^2 is much smaller than this (0.28).

Can someone please explain this if I'm on the wrong track. Thanks

 

[nate808]

Thank you for sharing your calculations and reasoning. Your approach seems to be correct. The value of \chi ^2 that you have calculated (0.28) is smaller than the critical value of 6.25, indicating that there is no significant deviation from the expected ratios in the offspring. This means that the observed data is in line with the expected ratios, and the cross between the two types of pea plants is not significantly different from what is expected based on Mendelian genetics.

In terms of relating the calculated value of \chi ^2 to the probability value in the distribution table, it is important to note that the probability value in the table represents the probability of obtaining a \chi ^2 value equal to or greater than the critical value, assuming that there is no true difference between the expected and observed values. In this case, since the calculated value of \chi ^2 is smaller than the critical value, the probability value is greater than 0.1, indicating that there is a high probability that the observed data is not significantly different from the expected ratios.

I hope this helps clarify your understanding. Keep up the good work as a scientist!