Write a linear model relating the DVBN levels in the shrimp to the immersion times, with an adjustment for the GL levels in the shrimp prior to ice glazing.

Refer to Exercise 16.12.

a. Based on your results in Exercise 16.12, test for differences in the mean level of DVBN across the five levels of immersion times.

b. Estimate the mean level of DVBN in shrimp having an immersion time of 20 seconds and a glycogen level of 3.0.

Exercise 16.12

The seafood industry is constantly experimenting with different methods for maintaining the quality of its product during storage. One such method used in the shrimp industry is ice glazing, where the shrimp are immersed in a salt-sugar solution at a low temperature, resulting in a thin layer of ice forming on the shrimp. The coating will hopefully limit the deterioration in the quality of shrimp if there is a deviation from the required storage temperature. An experiment was designed to study the effect of the length of time the shrimp were immersed in a container of cold water, the method by which the ice glaze is applied. The immersion times (IMTs) were 5, 10, 15, 20, and 25 seconds at a standard storage temperature of –25°C. To help control for the variation in shrimp characteristics, 5 shrimp were randomly selected from each of six batches of shrimp. The shrimp were then randomly assigned to one of the immersion times. A measure of the spoilage in frozen shrimp is the total volatile base nitrogen (TVBN) level in the shrimp. The TVBN level of each of the 30 shrimp was measured at the end of 135 days in storage. Previous studies have indicated that glycogen levels in the shrimp may have an effect on the development of spoilage over longer periods of storage. Thus, the glycogen levels (GL) in the 30 shrimp were measured prior to applying the ice glaze. The data from the study are given in the following table.

a. Write a linear model relating the DVBN levels in the shrimp to the immersion times, with an adjustment for the GL levels in the shrimp prior to ice glazing.

b. Using a scatterplot, does there appear to be straight-line relationship between the DVBN and GL levels in the shrimp? Make sure to take into account the six batches and IMT values.

c. Test the research hypothesis that there is a difference in the slopes relating DVBN to GL across the five values of IMT.

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