A student experiment was run to test the performance of 4 brands of batteries under 2 different Environments (room temperature and cold). For each of the 8 treatments, 2 batteries of a particular brand were put into a flashlight. The flashlight was then turned on and allowed to run until the light went out. The number of minutes the flashlight stayed on was recorded. Each treatment condition was run twice. Partial box plots showed:

An interaction plot showed:

An ANOVA table showed;

a) What are the main effect null and alternative hypotheses?
b) From the partial box plots, do you think that the Brand has an effect on the time the batteries last? How about the condition?
c) Do the conclusions of the ANOVA table match your intuition?
d) What does the interaction plot say about the performance of the brands?
e) Why might you be uncomfortable with a recommendation to go with the cheapest battery (brand C)?

" 175 140 s 130 120 110 120 100 F Cold Room temp Environment 200 Room temp 175 150 125t Cold 100 + Brand Sum of Mean Source DF Squares quare F-ratio P-value Envir Brand 3 338.187 112.729 2.9328 0.0994 Interaction 3 1278.19 426.063 11.085 0.0032 Error Total 15 32286.9 1 30363.1 303631 789.93