Question

An experimenter wishes to test if one of two types of fish food (a standard fish food and a new product) is better for producing fish of equal weight after a two-month feeding program. The experimenter has two identical fish tanks (1 and 2) and is considering how to assign 40 fish, each of which has a numbered tag, to the tanks. The best way to do this would be to

a. put all the odd-numbered fish in Tank 1 and the even-numbered fish in Tank 2. Give the standard food to Tank 1 and the new product to Tank 2.

b. obtain pairs of fish whose weights are roughly equal at the start of the experiment and randomly assign one of the pair to Tank 1 and the other to Tank 2. Give the standard food to Tank 1 and the new product to Tank 2.

c. proceed as in option (b), but put the heavier of each pair into Tank 2. Give the standard food to Tank 1 and the new product to Tank 2.

d. assign the fish completely at random to the two tanks using a coin flip: heads means Tank 1 and tails means Tank 2. Give the standard food to Tank 1 and the new product to Tank 2.

e. divide the 40 fish into two groups, with the 20 heaviest fish in one group. Randomly choose which tank to assign the heaviest fish and assign the lightest fish to the other tank. Give the standard food to Tank 1 and the new product to Tank 2.

Short answer

The correct answer is option (b) obtain pairs of fish whose weights are roughly equal at the start of the experiment and randomly assign one of the pair to Tank $1$and the other to Tank $2$. Give the standard food to Tank $1$and the new product to Tank $2$.

Step-by-step solution

Concept introduction

In quantitative tests, segmentation is the technique of selecting a predefined dataset from a huge population. Vary based on the type of assessment being undertaken, the measures taken to recruit from a general community may include simple chance picking or multi - stage sampling.

Explanation

We need to figure out the most efficient strategy to assign fish to the two identical fish tanks.

Looking at the possibilities, we can see that

Option (a) is not the best option because odd-numbered fish may have consistently higher or lower weights than even-numbered fish.

This suggests that the two groups will be different before the experiment begins, and we cannot be certain whether the differences observed after the treatment are attributable to the treatments or to the weight difference previous to the treatment.

Option (b) is a suitable option since the weights of the two groups will be similar, and the fish in each pair will be assigned to a treatment group at random.

Option (c) is not a suitable option because the fish in the second tank will weigh more than those in the first. This means that the two tanks will start off differently.

Option (d) is not a good option because the fish's weight is not taken into account.

Option (e) is not a suitable option because the fish in the second tank will be heavier than those in the first. This means that the two tanks will start off differently. As a result, option (b) is the proper choice.