Weights of parrot fish. A marine biologist wishes to use parrot fish for experimental purposes due to the belief that their weight is fairly stable (i.e., the variability in weights among parrot fish is small). The biologist randomly samples 10 parrot fish and finds that their mean weight is 6.3 pounds and the standard deviation is 2.4 pounds. The biologist will use the parrot fish only if there is evidence that the variance of their weights is less than 6.

a. Is there sufficient evidence for the biologist to claim that the variability in weights among parrot fish is small enough to justify their use in the experiment? Test at a = .01.

b. State any assumptions that are needed for the test mentioned in part a to be valid.