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Problem 1: An investigator is interested in the effects of stress on reaction time. She gives a reaction time test to three groups of subjects: one group that is under a great deal of stress, one group under a moderate amount of stress, and a third group that is under almost no stress. The data is presented below, and also provided in the Excel spreadsheet. This data is reaction times; therefore, a lower reaction time indicates that a subject performed better: High Stress Moderate Stress Low Stress 6 8 10 7 10 11 4 11 8 5 7 6 6 12 13 3 11 12 Theory A suggests that subjects under a moderate amount of stress will perform better than subjects in either the very low or the very high stress groups. Theory B predicts that subjects in the high stress group will perform better than subjects in either the low stress or the moderate stress groups. Theory C predicts that subjects in the moderate stress condition will perform significantly more poorly than subjects in the low stress condition. a. Using a significance level α = 0.05, perform the overall one-way ANOVA and then determine whether the data below provide evidence that the mean reaction time differs based on the level of stress. Provide your ANOVA table. b. If the results from part (a) show that there is a difference in the mean reaction time for varying stress levels, perform additional analysis to test whether Theory A, Theory B, or Theory C is accurate or if none of them can be shown to be accurate. State your conclusion and provide the appropriate test statistics. Again, you should use a significance α = 0.05. Problem 2: Everyone has heard the adage that “you can’t teach an old dog new tricks.” In an attempt to demonstrate that it is harder to teach an old dog new tricks versus a puppy, a researcher went to the pound and adopted 15 old dogs and 15 puppies. The researcher then attempted to teach each of the 30 dogs one of the standard dog tricks, "sit", "stay", and "roll over." The researcher taught only one trick to each dog and keep a record of how many days it takes before they learned the tricks. The results of the experiment are listed in the table below, and also provided in the Excel spreadsheet: Sit Shake Roll Over Puppies 2 4 6 1 5 9 3 4 7 1 6 8 2 7 10 Old Dogs 2 9 13 5 10 12 2 11 15 4 13 17 3 7 13 Based on this data, conduct a two-way analysis of variance to determine if it is more difficult for old dogs to learn new tricks compared to puppies. Create an interaction graph as part of your solution.

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