Cotton versus Cucumber In Exercise 11.65, you used the analysis of variance procedur...

Cotton versus Cucumber In Exercise 11.65, you used the analysis of variance procedure to analyze a 2 × 3 factorial experiment in which each factor–level combination was replicated five times. The experiment involved the number of eggs laid by caged female whiteflies on two different plants at three different temperature levels. Suppose that several of the whiteflies died before the experiment was completed, so that the number of replications was no longer the same for each treatment. The analysis of variance formulas of Chapter 11 can no longer be used, but the experiment can be analysed using a multiple regression analysis. The results of this 2 × 3 factorial experiment with unequal replications are shown in the table

a. Write a model to analyze this experiment. Make sure to include a term for the interaction between plant and temperature.

b. Use a computer software package to perform the multiple regression analysis.

c. Do the data provide sufficient evidence to indicate that the effect of temperature on the number of eggs laid is different depending on the type of plant?

d. Based on the results of part c, do you suggest refitting a different model? If so, rerun the regression analysis using the new model and analyze the printout.

e. Write a paragraph summarizing the results of your analyses.

Reference:

The Whitefly in California The whitefly, which causes defoliation of shrubs and trees and a reduction in salable crop yields, has emerged as a pest in Southern California. In a study to determine factors that affect the life cycle of the whitefly, an experiment was conducted in which whiteflies were placed on two different types of plants at three different temperatures. The observation of interest was the total number of eggs laid by caged females under one of the six possible treatment combinations. Each treatment combination was run using five cages.

a. What type of experimental design has been used?

b. Do the data provide sufficient evidence to indicate that the effect of temperature on the number of eggs laid is different depending on the type of plant? Use the printout to test the appropriate hypothesis.

c. Plot the treatment means for cotton as a function of temperature. Plot the treatment means for cucumber as a function of temperature. Comment on the similarity or difference in these two plots.

d. Find the mean number of eggs laid on cotton and cucumber based on 15 observations each. Calculate a 95% confidence interval for the difference in the underlying population means.