Reproduction in sea urchins involves the release of sperm and eggs in the open ocean. Fertilization begins when a sperm bumps into an egg and the sperm protein bindin attaches to recognition sites on the egg surface. Gene sequences of bindin and egg-surface proteins vary greatly between closely related urchin species, and eggs can identify and discriminate between different sperm. In the burrowing sea urchin, Echinometra mathaei, the protein sequence for bindin varies even between populations within the same species. Do these differences affect fertilization? To test this, Palumbi (1999) carried out trials in which a mixture of sperm from AA and BB males, referring to two populations differing in bindin gene sequence, were added to dishes containing eggs from a female from either the AA or the BB population. The results below indicate the fraction of fertilizations of eggs of each of the two types by AA sperm (remaining eggs were fertilized by BB sperm).

a. Plot the data using a method other than the box plot. Is there an association in these data between female type and fertilizations by AA sperm?

b. Inspect the plot. On this basis, which method from this chapter (mean or median) would be best to compare the locations of the frequency distributions for the two groups? Explain your reasoning. Calculate and compare locations using this method.

c. Which method would be best to compare the spread of the frequency distributions for the two groups? Explain your reasoning. Calculate and compare spread using this method.

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AA females: 0.58,0.58, 0.59,0.59, 0.69,0.69, 0.72,0.72, 0.78,0.78, 0.78,0.78, 0.81,0.81, 0.85,0.85, 0.85, 0.85, 0.92,0.92, 0.93,0.93, 0.950.95 BB females: 0.15,0.15, 0.22,0.22, 0.30.0.30, 0.37,0.37, 0.38,0.38, 0.50,0.50, 0.950.95