On the basis of size, blue crabs are categorized by marine biologists as young, juvenile, mature. In a healthy crab population that is being acceptably harvested by commercial fishermen, the percentage of each type is

50% young 30% juvenile 20% mature

Deviations from these percentages usually indicate an unhealthy or overfished population. Fish and game biologists can dredge the bottom of a bay or estuary with nets to obtain a sample of crabs in an area close to commercial crabbing to determine if there is an unacceptable distribution of ages. Suppose that a small bay is dredged and the following categories of crab are netted:

58 young 33 juvenile 39 mature

a. Give the most logical null and alternative hypotheses for this study.

b. For this study, which is more serious, a Type I or Type II error? Why?

c. Perform a test of significance at a = 0.05.

d. What is the experimental conclusion?

e. Suppose it is known that fishermen keep all mature and some juvenile crabs they net; all others are released unharmed. It is also known that young crabs are most susceptible to pollution, with juveniles the second most susceptible. Based on this information and the test of significance, which of the following is the appropriate action?

i. Allow continued harvesting of crabs in the bay.

ii. Close the bay to commercial crabbing because of overfishing.

iii. Close the bay due to possible pollution.

iv. Close the bay because of both overfishing and possible pollution.