Chapter 16.3, Problem 49E

Copepod Cuisine. Copepods are tiny crustaceans that are an essential link in the estuarine food web. Marine scientists C. Weiss et al. at the Chesapeake Biological Laboratory in Maryland designed an experiment to determine whether dietary lipid (fat) content is important in the population growth of a Chesapeake Bay copepod. Their findings were published as the paper “Development and Lipid Composition of the Harpacticoid Copepod Nitocra Spinipes Reared on Different Diets” (Marine Ecology Progress Series, Vol. 132, pp. 57-61). Independent random samples of copepods were placed in containers containing lipid-rich diatoms, bacteria, or leafy macroalgae. There were 12 containers total with four replicates per diet. Five gravid (egg-bearing) females were placed in each container. After 14 days, the number of copepods in each container were as follows.

Diatoms	Bacteria	Macroalgae
426	303	277
467	301	324
438	293	302
497	328	272

At the 5% significance level, do the data provide sufficient evidence to conclude that a difference exists in mean number of copepods among the three different diets? (Note: T₁ = 1828, T₂ = 1225, T₃ = 175, and ${\displaystyle \sum x_i^2=1,561,154.}$)