2. The effect of caffeine levels on performing a simple finger tapping task was investigated in a double blind study. Thirty male college students were trained in finger tapping and randomly assigned to receive three different doses of caffeine (0, 100, or 200 mg) with 10 students per dose group. Two hours following the caffeine treatment, students were asked to finger tap and the numbers of taps per minute were counted. The data are tabulated below. Caffeine Dose Finger Taps per Minute 0 mg 242 245 244 248 247 248 242 244 246 242 100 mg 248 246 245 247 248 250 247 246 243 244 200 mg 246 248 250 252 248 250 246 248 245 250 (a) (8 points) Use the R script to make side-by-side boxplots for the three groups. Do these plots indicate any obvious differences between the groups? (b) (8 points) Use the R script to construct an ANOVA table and test whether there are significant differences in finger tapping between the students treated with different doses of caffeine. Use o = 0.10. Interpret your results. (c) (8 points) Use the R script to check the normality and constant variance assumptions by making residual plots. (d) (8 points) Use the R script to check the normality and constant variance assumptions by implementing the Shapiro-Wilk test and the Bartlett's test. (e) (10 points) Use the R script to compare finger tap rates of the 100 mg and 200 mg caffeine groups with the control group using Bonferroni's method with a = 0.10. Interpret the results