To study the effectiveness of treatments for insomnia, a sleep researcher conducted a study with 12 participants. Four participants were instructed to count sheep (Sheep Condition), four were told to concentrate on their breathing (Breathing Condition), and four were not given any special instructions. Over the next few days, measures were taken of how many minutes it took each participant to fall asleep. The average times for the participants in the Sheep Condition were 14, 28, 27, and 31; for those in the Breathing Condition, 25, 22, 17, and 14; and for those in the control condition, 45, 33, 30, and 41.
Do these results suggest that the different techniques have different effects?
(Use the .05 significance level.)
a. Use the five steps of hypothesis testing.
b. Sketch the distribution involved.
c. Figure the effect size of the study.
d. Explain your findings (including the logic of comparing within-group to between-group population variance estimates, how each of these is figured, and the F distribution).