Question

Copepod Cuisine. Copepods are tiny crustaceans that are an essential link in the estuarine food web. Marine scientists G. 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 in 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 was $12$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 was as follows.

At the $5\%$ significance level, do the data provide sufficient evidence to conclude that a difference exists in the mean number of copepods among the three different diets? (Note:$T_1=1828,T_2=1225,T_3=1175,$$\Sigma x_i^2=1,561,154.)$

Short answer

The given data has a tendency to reject $H_0$. The data on the number of copepods that use three different diets provide enough information at the $5\%$ level to determine that there is a difference in the mean number of copepods that utilise three different diets.

Step-by-step solution

Given information

The given data is

$T_1=1828$

$T_2=1225$

$T_3=1175$

$\Sigma x_i^2=1,561,154$.

Explanation

From the given data

${\mathrm{H}}_0:{\mu }_1={\mu }_2={\mu }_3$

$H_a:$Not all the mean are equal

The value of $a=0.05$

Calculate the value of the test statistic

$\mathrm{F}=\mathrm{MSTR}/\mathrm{MSE}$

$F=54.58$

The value of critical value is $4.26$

Here the test statistic > critical value

$p<a$

It has a tendency to reject $H_0$. The data on the number of copepods that use three different diets provide enough information at the level to determine that there is a difference in the mean number of copepods that utilise three different diets.