General instructions. Please write your full name at the top of every page you hand in. Please collate and staple your pages together. Please write clearly and thoroughly explain all your computations; an unannotated series of formulas that mysteriously ends up with the correct number will not be given full credit. When doing the homework, you are encouraged to use all resources at your disposal to the extent that they help you learn the material; nevertheless, you must write your own answers in your own words.

1. (6 pts.) p. 128, #12.
   ALSO characterize the effect size by computing f_adj.

2. (6 pts.) p. 128, #14.
   BUT do it for a desired power of .9, not for .8.

3. (8 pts.) Regarding #10, p. 127. Consider the difference in cortical weights, that is, the difference Experimental-Control for the matched littermates. (You can use SPSS to determine the difference; use Transform -> Compute.) There are 12 such differences in each of the three Experiment groups. The three Experiment groups were run at different times of year.
     Suppose we believe that the time of year does have an effect, however small, on the difference in cortical weights. We want to run an experiment that has high probability of detecting the effect of time of year; that is, we want to reject the null hypothesis that time of year has no effect on the difference in weights. Use the data from #10 (p. 127) to determine the sample size we need for a power of .9.
     Suppose you are reviewing a grant application. The investigator describes an intriguing and insightful theory that predicts there should be an effect of time of year on the difference in cortical weights. The investigator includes the #10, p.127 data in his proposal, citing them as pilot data which show a small but promising hint of an effect. Would you recommend funding the proposal? Why or why not?