11.55 Crossing peas When crossing round (R) and yellow (Y)

peas with wrinkled (W) and green (G) peas, one can get any combination of color and appearance, denoted here as RY, RG, WY and WG, but traits round and yellow are dominant. In particular, Gregor Mendel postulated that these four possible combinations would appear in the ratio 9:3:3:1. From an experiment involving 556 such crossings, 315 were RY, 108 RG, 101 WY and 32 WG.

a. Construct a table showing these counts.

b. If Mendel’s theory about the ratio 9:3:3:2 is correct, how likely is each combination to occur? (Hint: Of 9 + 3 + 3 + 1 = 16 crossings, how many are of type RY?)

c. Find the expected values for the four combinations assuming Mendel’s theory is correct.

d. A chi-squared test for testing Mendel’s theory will be based on how many degrees of freedom?

e. The chi-squared statistic for these data equals 0.47.

Will the P-value for the test be large or small? Why?