(Solved): 3. We wish to compare the reaction time to a loud sound for humans who are given Water, Energy Drin ...

3. We wish to compare the reaction time to a loud sound for humans who are given Water, Energy Drink A, or Energy Drink B shortly before the sound is played. Let \\( \\mu_{1}, \\mu_{2}, \\mu_{3} \\) be the true mean reaction time for humans who have had Water, Energy A, Energy Drink B, respectively. The following are the summary statistics for each treatment and the ANOVA table: Anova: Single Factor Summary ANOVA (a) To test if there is a difference in mean reaction time for humans having Energy Drink A and Energy Drink B, we use the Fisher's Least Significance Difference (LSD) Method. \\( H_{0}: \\mu_{1}=\\mu_{2}, H_{1}: \\mu_{1} \\neq \\mu_{2} \\) Compute the value of the test statistic. (b) If we want to compare all possible pairs of mean differences using an experimentwise \\( \\alpha \\) of 0.05 , what should the comparison-wise \\( \\alpha \\) be for each of the comparisons?