Use a calculato to calculate ${}^2$ in the two examples that follow. The ${}^2$ values you should obtain are given. If the value you obtain does not agree with the value given, repeat the calculation until agree ment is reached. Notice how the ${}^2$ calculated is interpreted.

In a cross involving Drosophila melanogaster, an $F_2$ population included $272$ flies with long $($normal$)$ wings and $60$ flies with dumpy wings. Calculate ${}^2$ and fill in the blanks below. Do these results approximate a $3$:$1$ ratio?

a$.$ In interpreting this ${}^2$ value, you have degrees of freedom.

b$.$ In this case, do you accept$/$reject the hypothesis that these data approximate a $3$:$1$ ratio?

c$.$What is the probability that the deviations are due to chance alone?