The two claws of the lobster (Homarus americanus) are identical in the juvenile stages. By adulthood, however, the two claws normally have differentiated into a stout claw called a "crusher" and a slender claw called a "cutter." In a study of the differentiation process, 26 juvenile lobsters were reared in smooth plastic trays and 18 were reared in trays containing oyster chips (which they could use to exercise their claws). Another 23 lobsters were reared in trays containing only one oyster chip. The claw configurations of all the lobsters as adults are summarized in the table.

(a) The value of the contingency-table chi-square statistic for these data is χ2s = 24.35. Carry out the chi-square test at α = 0.01.
(b) Verify the value of χ2s given in part (a).
(c) Construct a table showing the percentage distribution of claw configurations for each of the three treatments.
(d) Interpret the table from part (c): In what way is claw configuration related to treatment? (For example, if you wanted a lobster with two cutter claws, which treatment would you choose and why?)

Transcribed Image Text:

Claw configuration Treatment Right Right Right crusher, cutter, cutter, Left LeftLeft cutter crusher cutter Oyster chips Smooth plastic2 One oyster chip 7 20