A scientist studied the effect of amount of fertilizer and a

A scientist studied the effect of amount of fertilizer and amount of moisture on the yield of a new tomato hybrid. The investigation was carried out in a greenhouse where the two factors of interest could be precisely controlled. Two fertilizer levels (10 and 20 units) and three moisture levels (1,2, and 3 inches) were considered. Eight pots of tomato plants were randomly assigned to each fertilizer/moisture combination. The sample means of the 8 yields associated with each fertilizer/moisture combination are provided in the tables below. The residual sum of squares for these data is 2607.5. You may assume that all of the required assumptions are satisfied for this data set. In fact, the data is not from an experiment as described above. Instead, it has been randomly generated from a model in such a way that all the assumptions are satisfied. Conduct a One-way Analysis of Variance F-test for these data to test the null hypothesis that all treatment means are equal. Use each combination of fertilizer amount and moisture amount as a treatment, and report a test statistic, its degrees of freedom, a p-value, and a conclusion in context. Does there appear to be a significant interaction between fertilizer amount and amount of moisture? Draw a graph of the sample means (by hand, or using software) that illustrates the evidence or lack of evidence of a significant interaction. Clearly explain how the graph you\'ve drawn supports evidence/lack of evidence of an interaction. Regardless of your answer in part (¡TB|), assume there is no significant interaction between the two factors in this experiment. Estimate the main effect of fertilizer, and its corresponding standard error. Show all your work. Is there a significant effect on yield due to the amount of fertilizer? Conduct an appropriate statistical test to answer this question. Give the null and alternative hypotheses, test statistic, p-value, and conclusion. Show all your work. Write down the null and alternative hypotheses for a test of a significant moisture main effect. What is an alternative approach to that presented here, in which we could easily test for a significant effect to due moisture amount? In models where a significant interaction is present, explain why the main effects of moisture and fertilizer may no longer be of much interest.

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