To test if the observed results of 787 green and 277 yellow pods in the F2 generation of the pea plant cross agree with the expected ratio of 3:1, we can use the Chi-square test.
The Chi-square test formula for goodness of fit is:
χ^2 = Σ [(O - E)^2 / E]
Where:
χ^2 = Chi-square value
O = Observed frequency
E = Expected frequency
First, let's calculate the expected frequencies based on the expected ratio of 3:1:
Total observed frequency = 787 + 277 = 1064
Expected frequency for green pods = (3/4) * 1064 = 798
Expected frequency for yellow pods = (1/4) * 1064 = 266
Now, let's calculate the Chi-square value:
χ^2 = [(787 - 798)^2 / 798] + [(277 - 266)^2 / 266]
= [(-11)^2 / 798] + [(11)^2 / 266]
= 0.167 + 0.449
= 0.616
Since we have 1 degree of freedom (df = 2 - 1 = 1), we can compare the calculated Chi-square value of 0.616 to the critical Chi-square value of 3.84 at the 5% level of significance.
Since the calculated Chi-square value (0.616) is less than the critical Chi-square value (3.84), we fail to reject the null hypothesis. This means that the observed results of 787 green and 277 yellow pods in the F2 generation are not significantly different from the expected ratio of 3:1 at the 5% significance level.
If you have any more questions, feel free to ask!