Rest in fruit flies, Drosophila melanogaster, has many features in common with mammalian sleep. Its study might lead to a better understanding of sleep in mammals, including humans. Hendricks et al. (2001) examined the role of the signaling molecule cyclic AMP (cAMP) by comparing the mean number of hours of resting in six different lines of mutant or transgenic fly lines having different levels of cAMP expression. Measurements are hours per 24 hours divided by the mean of “wild type” flies. Means (±SE) are shown for the different fly lines in the accompanying graph.

a. Write the statement of the linear model to be fit to these data to compare means between groups. Indicate what each term in the model represents.

b. Write the corresponding statement for the null hypothesis of no differences between mutant lines.

c. Using a ruler, add the predicted values for each model to the figure (approximate positions will suffice).

d. What test statistic should be used to test whether the null model should be rejected in favor of the alternative?