Investigators wished to know if the oxygen consumption rates (mL/(mg*min) varied between two species of limpets, Acmaea scabra (AS) and Acmaea digitalis (AD), at three concentrations of seawater. The three concentrations of seawater were 100%, 75%, and 50%. The two species of limpets are known as ribbed limpets, they are sea snails (a type of marine gastropod mollusk). Import the following data set:

limp=read.csv('https://www.dropbox.com/s/n306atkd4h2cm8a/limpet.txt?dl=1',header=T, sep=',') attach(limp)

Regardless of whether or not the Assumptions for the test are met, all parts below!!!

(a) Make side-by-side boxplots for each factor in the same graphing window as we did in lecture. Can you tell from this what factor(s) may be significant? Comment on what you see.

(b) Make a residual vs. fitted plot, a Q-Q plot , and run a Levene's test for homogeneity for the full model two-way ANOVA. Do the assumptions of ANOVA appear to be valid? In other words, are the data approximately normal with even spread? Make sure you comment on these graphs and the Levene Test!

(c) Fit a two-way ANOVA model with interactions (aka The Full Model). What are the null and alternative hypotheses for the test on the interaction effect? Is there a significant interaction effect between species typeand water concentration?

(d) Make an interaction plot to support the result of (c). What does this plot tell you? I recommend inputting the species factor before the waterconc factor for a better looking plot.

(e) Regardless of whether or not you found an interaction effect between the factors, doa hypothesis test for the main effects of the species and water concentration factors by redoing your ANOVA model (that is run the ANOVA using the additive model by removing the interaction term). 1. Is there a significant difference in the mean oxygen consumption rate between the 2 species? Give me the hypotheses, a p-value and conclusion for your results. 2. Is there a significant difference in the mean oxygen consumption rate between the 3 water concentration percentages? Give me the hypotheses, a p-value and conclusion for your results.

(f) Run Tukey's HSD multiple comparison on any factor(s) that were significant in part (e) (Hint: Only one of the factors should have been significant). Give me the Tukey output and interpret any intervals that had a P-value less than 0.05. What do you conclude overall about this study?