Question

Case Study: Sampling Scallops [from Barnett 1995 and McClave, Benson and Sincich 1998] "The US Fisheries and Wildlife Service requires that in any given 'harvest,' the average meat per scallop at least 1/36 of a pound. The requirement is aimed at protecting baby scallops, though less to guarantee them happy childhoods than to preserve enough adult scallops so that the species does not disappear.

"The vessel arrived at a Massachusetts port with 11,000 bags of scallops, from which the harbormaster randomly selected 18 bags for weighing. From each such bag, his agents took a large scoopful of scallops; then, to estimate the bag's average meat per scallop, they divided the total weight of meat in the scoopful by the number of scallops it contained. Based on the 18 statistics thus generated, the harbormaster estimated that each of the ship's scallops possessed on average 1/39 of a pound of meat (that is, they were about seven percent lighter than the minimum requirement). Viewing this outcome as conclusive evidence that the weight standard had been violated, federal authorities at once confiscated 95 percent of the catch (which they then sold in an auction). The fishing voyage was thus transformed into a financial catastrophe for its participants.

"The ship's owner was as displeased with the US government as Captain Ahab had been with Moby Dick. He declared that the vessel had fully complied with the weight standard and saw lunacy in the assertion that sampling 18 bags out of 11,000 could yield a reliable estimate of the mean weight of all the ship's scallops. He filed a lawsuit against the government and arranged for a Boston law firm to represent him."

The law firm would like you to evaluate whether the ship’s owner has cause to file a lawsuit against the federal government. Included below are the actual scallop weight measurements for each of the 18 sampled bags. For ease of understanding, each number is expressed as a multiple of 1/36 of a pound, the minimum permissible average weight per scallop. Consequently, numbers below one indicate individual bags that do not meet the standard:

        0.93    0.88    0.85    0.91    0.91    0.84    0.90    0.98    0.88
        0.89    0.98    0.87    0.91    0.92    0.99    1.14    1.06    0.93

Among the questions you should answer are:

a.) Can a reliable estimate of the mean weight of all the scallops be obtained from a sample size of 18? If not, how big a sample would give a reliable estimate?

b.) Are there any statistical flaws in the government’s decision rule to confiscate a scallop catch if the mean weight of the scallops is less than 1/36 of a pound?

c.) Is there another procedure for determining whether a ship is in violation of the minimum weight restriction? Apply your procedure to the data, and draw a conclusion about the ship in question.

Answer 1