Willam E. Pelham et al. studied the how different levels of Ritalin and Adderall had on a child's ability to follow rules when the child is diagnosed with attention deficit hyperactivity disorder, or ADHD. The study involved the random assignment of children to one of five treatment groups: placebo, 10 mg Ritalin, 17.5 mg of Ritalin, 7.5 mg of Adderall, or 12.5 mg of Adderall. Each child was to take their treatment twice a day. The response variable was a score which measured the child's ability to follow rules. The higher the score, the better the ability the child has to follow the rules. The data can be found in the Download .csv file. Use a : 0.05 for any statistical tests. You will have to stack the data, try using the R command stack(data[216])...if you named the data file, data. (a) Using the technology available to you, create boxplots of the data. What do these boxplots tell you about the variation in the score between the different treatments? Choose the most appropriate answer. A. The variation in a child's score seems to depend on the treatment. B. The variation in a child's score does not seem to depend on the treatment. 0. The Normal distribution condition of the score does not seem to hold here - a childs score is not Normally distributed for each of the five treatments. D. The Normal distribution condition of the score seems to hold a childs score is Normally distributed for each of the five treatments. (b) Does this data suggest that the variance of a childs score is the same for all treatments? Find the value of the test statistic and its Pvalue and base your decision on a = 0.05. Test Statistic = D (use at least two decimals in your answer) P-value = [3 (use at least four decimals in your answer) (c) Does the data indicate that a childs score is the same for each of the five treatments? Select the appropriate statistical hypotheses below, and in doing so consider your findings in part (b). A- H0 1 Pzaceba : mmmmg : Rital'LSmg : Add7.5mg : Add12.5mg HA I at least one [71- is different 5- H0 1 liPlacebo : @italmg : gtmzsmg : HdZSmg : HAlzmg HA ; \"Placebo 7' \"Rimming 7 HRitalTEmg 7 HAdd7.5mg 7 MAdd12.5mg c- H0 2 XPlacebn : XRilalOmg : XRital7.5mg : XAdd7.5mg : XAddlZmg HA I at 16351; one Xi is different 9- H0 1 \"Placebo = #Rimmmg = HRita17.5mg = HAddTEvmg = HAdd12.5mg HA I at least one ['1' is different Test Statistic = C] (use at least two decimals in your answer) Pvalue = C] (use at least four decimals in your answer) (e) Estimate the standard deviation in an ADHD childs score, using at least two decimals. E] (f, i) Using a familywise error rate of a : 0.05 to assist in your analysis, locate the treatment(s) that improve an ADHD childs score. Find the cutoff value: i MSE'(i -l- i) for the observed differences. "1 "J Uwse at least two decimals) Find the q : q(km,k)value: where k : number of treatments and n : total number of observations. Uwse at least two decimals) (fii) Use Software to perform a Tukey HSD, Post Hoc analysis. Use a 95% confidence level and give at least 4 digits in all answers. When looking at the difference: PlaceboAdderall 12.5mg the lower limit for the difference is C] and the upper limit is C]. Based on the data the first treatment listed is Larger than then the second treatment listed. When looking at the difference: Ritalin 10mgAdderall 7.5mg the lower limit for the difference is C] and the upper limit is C]. Based on the data the first treatment listed is Larger than t then the second treatment listed. (fiii) Based only on the correct ANOVA and Post Hoc analysis of the above data, does the treatment influence the outcome? Yes 4