The degrees of freedom for the chi-square goodness-of-fit test are n — 1, where n equals the number of expected classes. There are two expected classes (black and white) so the degree of freedom is 2 — 1 = 1. On the basis of the calculated chi-square value in Table 3.4, the probability associated with this chi-square is greater than .05 (the critical probability for rejecting the hypothesis that chance might be responsible for the differences between observed and expected numbers); so the black and white progeny appear to be in the 1: 1 ratio expected in a testcross.

Next, compute a second chi-square value comparing the number of straight and wavy progeny with the numbers expected from the testcross. From the Vv X vv, 1/2 Vv (straight) and 1/2 vv (wavy) progeny are expected:

In Table 3.4, the associated probability is much less than .05, indicating that chance is very unlikely to be responsible for the differences between the observed numbers and the numbers expected with independent assortment. The genes for coat color and hair type have therefore not assorted independently.

(b) To determine the recombination frequencies, identify the recombinant progeny. Using the notation for linked genes, write the crosses:

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