A fish hatching experiment involved multiple eggs within each of multiple clutches (group of eggs produced by a single hen). A total of 21 clutches were assigned to one of three treatments: (1) carbon dioxide and oxygen removed, (2) carbon dioxide only removed, and (3) neither removed. That is, each treatment was applied to 7 clutches. The parameter of interest is the probability that an egg hatched.

(a) State an appropriate model for this situation, including any relevant assumptions about independence or correlation.

(b) Interpret the parameters of your model above. In particular, which parameters are of most interest in the test for whether there's a treatment effect on the hatching probability?