Question

Researchers used a standard fish seine to sample the fish population of Mason Pond. Most of these fish were bluegill (Lepomis macrochirus). Researchers removed fish from the seine and measured these fish on a fish board the boat. Researchers measured each fish to the nearest millimeter. Then, researchers measured all of the fish brought in by your seine, except for fish less than 15 mm.   

Size Category	Observed	Expected
15-35 mm	22	7.33
>35-55 mm	16	5.33
>55 mm	6	2

1. As indicated above, test the null hypothesis that the fish size classes are evenly distributed using a chi-square analysis. Did our seine sample adequately test the fish population for the entire pond? Why or why not? If fish sizes are not evenly distributed, what ecological factors could explain this uneven distribution?

Answer 1

We are given the following data and are asked to test the hypothesis that the fish size classes are evenly distributed using a chi-square analysis.

Size Category	Observed	Expected
15-35mm	22	7.33
>35-55mm	16	5.33
>55mm	6	2

Null hypothesis

H₀: fish size classes are evenly distributed

Alternate hypothesis

H₁: fish size classes are not evenly distributed.

Test statistic under H₀:

Size Category	Observed	Expected	Observed-Expected	(Observed-Expected)2/Expected
15-35mm	22	7.33	14.67	29.36
>35-55mm	16	5.33	10.67	21.36
>55mm	6	2	4	8

Inference

at 5% level of significance and at 4 d.f. from tables

, null hypothesis may be rejected.

Hence we conclude that the fish size classes are not evenly distributed i.e., our seine sample did not adequately test the fish population for the entire pond.

One of the ecological factors could be overfishing for fishes who have the largest size. Another factor could be trophy hunting i.e., hunting fishes which have the largest size and weight.