Building on the cup experiment of the Chapter 4 Step-By-Step, a student selects one type of container and designs an experiment to see whether the type of Liquid stored and the outside Environment affect the ability of a cup to maintain temperature. He randomly chooses an experimental condition and runs each twice:

After fitting a two-way ANOVA model, he obtains the following interaction plot, ANOVA table, and effects table:

a) State the null and alternative hypotheses.
b) Test the hypotheses at ( = 0.05.
c) Perform a residual analysis.
d) Summarize your findings.

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Change in Temperature 13 14 31 31 Environment Liquid Water Water Water Water Coffee Coffee Coffee Coffee Room Room Outside Outside Room Room Outside Outside 27 29 e Water Outside Room Environment Sum of Mean Source DF Squares Square F-ratio P-value Liquid Environ 595.125 595.125 952.2 <0.000)1 Interaction 0125 0.125 02 0.6779 Error Total 1 15.125 15.125 24.2 0.0079 4 2.500 0.625 7 612.875 Estimate 20.875 -1.375 1.375 8.625 -8.625 Term Overall mean Liquid II ICoffee] Liquid II (Water Environment Il [Outside] Environment吒Room]