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.

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