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16. (18 points) A study is performed to investigate the effects of three different studying techniques - or "treatments" - vs. a control on 500 people. The outcome of interest is an improvement score (out of 125 points), reported by the student. In the table below, the mean and standard deviation of the improvement score for each treatment category is reported. Mean SD Group Control 60.93 19.87 56.66 18.39 Treatment 1: Despair (tx1) Treatment 2: Frequent Gaming Breaks (tx2) Treatment 3: 4am Cramming (tx3) 64.51 19.53 70.61 17.55 (a) Based on this information, perform three separate hypothesis tests investigating: H : Mc - Mtr = 0; H: Mc - Mto # 0 for each treatment group against the control group. Use a=0.10. (b) As a more sophisticated data scientist, you instead use a regression model. Your results for the coefficients of the model are: Estimate Std. error t-value Pval Group (Intercept) 60.756 1.678 36.209