Biofloc system. The biofloc technology (BFT) has recently gained attention as an economic and environmentally sustainable production system for aquatic species. In this system, bacteria convert fish waste into microbial biomass (biofloc), thereby improving the water quality in fish tanks and reducing the water use. Research published in Aquaculture (Vol. 521, 2020) evaluated the growth performance, survival, gill lesions, body composition, nutritional value of the floc, and clinical biochemistry variables of Nile tilapia for 112 days. From the growth performance of Nile tilapia reared in a zero exchange biofloc system, a quadratic relationship was observed between final biomass weight (in kg) (y) and density (fish m-3 ) (x) as shown below. Independent Variable b Estimate p-Value x 383.26 6 0.001 x2 -3.72 6 0.001 Model R2 = 0.88

a. Conduct a test of overall model utility. Use a = .05.

b. The researchers hypothesized that final biomass weight increases at a decreasing rate with density. Set up the null and alternative hypotheses to test this theory.

c. Use the reported results to conduct the test, part

b. Give your conclusion (at a = .05) in the words of the problem.