In the early days of genetics, scientists realized that Mendel’s laws of segregation could be used to predict that the second generation after a cross between two pure strains (the F₂ ) ought to have greater variance than the first generation after the cross (the F₁ ). One early test of this prediction was done by measuring flower length in a cross between two varieties of tobacco (East 1916). The following is a frequency table of the resulting individuals in both the first and second generations:

a. Show how the means and variances were calculated for the F₁ data.

b. Test whether the variances of the two groups of plants differ, making all necessary assumptions. Is one significantly greater than the other? If so, which one?

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Flower length (mm) 5252 5555 5858 6161 6464 6767 7070 7373 7676 7979 8282 8585 Number of F1F₁ plants 00 44 1010 4141 7575 4040 33 00 00 8 8 8 Number of F2F2 plants 33 99 1818 4747 5555 9393 7575 6060 4343 2525 77 88