Refer to Exercise 17.37. a. For meat products, separate the four assessment methods into groups…

Refer to Exercise 17.37.

a. For meat products, separate the four assessment methods into groups such that all assessment methods in a group are not significantly different from one another with respect to their mean e. coli levels. Use an experimentwise error rate of a  .05.

b. For fruit products, separate the four assessment methods into groups such that all assessment methods in a group are not significantly different from one another with respect to their mean e. coli levels. Use an experimentwise error rate of a  .05.

c. For vegetable products, separate the four assessment methods into groups such that all assessment methods in a group are not significantly different from one another with respect to their mean e. coli levels. Use an experimentwise error rate of a  .05.

d. Provide a 95% confidence interval on the mean e. coli level of a container of meat for each of the assessment methods.

e. Provide a 95% confidence interval on the mean e. coli level of a container of fruit for each of the assessment methods.

f. Provide a 95% confidence interval on the mean e. coli level of a container of vegetables for each of the assessment methods.

g. Was it necessary to do a separate grouping of the assessment methods for each of the food types? Justify your answer based on the tests conducted in the AOV table.

Exercise 17.37

A state health department conducted an experiment to evaluate the reliability of assessing the level of contamination of e. coli in three food sources, meat, fruit, and vegetables. There are four unique methods for assessing e. coli—M1, M2, M3, and M4—and hundreds of laboratories that use one or more of theses methods in the United States. For each of the methods of assessment, five laboratories are randomly selected to participate in the study. Forty containers are prepared for each food source by spiking the container with a known level of contamination of e. coli and then placing the container in a controlled climate for 3 weeks to allow the e. coli level to stabilize. Six containers, two of each of the three food sources, are then sent to each of the 20 laboratories selected for the study. The e. coli level (cfu/g), Yijkl, determined by the kth lab using assessment method j for the lth container of food source i is recorded for each of the 120 containers. The health department wants to compare the mean e. coli levels of the four assessment methods and their differences across the food sources. It also wants to determine if there are major differences in the mean e. coli determinations across the many laboratories in the United States.

 a. Write a model that displays an appropriate relationship between a level of contamination, Yijkl, and its possible sources of variation. Include any restrictions on the parameters in your model and any distributional properties of the random variables in your model.

b. Do the necessary conditions for testing hypotheses and constructing confidence intervals appear to be satisfied? Justify your answers.

c. Construct an ANOVA table for this experiment. Make sure to include expected mean squares and the p-values for the F tests.

d. At the   .05 level, which main effects and interaction effects are significant? Justify your answer by including the relevant p-values.

e. What are your overall conclusions about the differences in the four assessment methods?

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