In the garden pea Pisum sativum, seed color can be yellow (Y) or green (G), and seed shape can be round (R) or wrinkled (W). Consider the following three hypotheses describing a population of plants:
H(1)0: Pr{Y} = 3/4
H(2)0: Pr{R} = 3/4
H(3)0: Pr{Y} = Pr{R | G}
The first hypothesis asserts that yellow and green plants occur in a 3:1 ratio; the second hypothesis asserts that round and wrinkled plants occur in a 3:1 ratio, and the third hypothesis asserts that color and shape are independent. (In fact, for a population of plants produced by a certain cross-the dihybrid cross-all three hypotheses are known to be true.)
Suppose a random sample of 1,600 plants is to be observed, with the data to be arranged in the following contingency table:

Invent fictitious data sets as specified, and verify each answer by calculating the estimated conditional probabilities.
(a) A data set that agrees perfectly with H(1)0, H(2)0 and H(3)0
(b) A data set that agrees perfectly with H(1)0 and H(2)0 but not with H(3)0
(c) A data set that agrees perfectly with H(3)0 but not with H(1)0 or H(2)0.

Transcribed Image Text:

Color Y G Shape R 1.600