Experimental design question

Q 22. The Effectiveness of a New Migraine Pill: A study is conducted to de- termine the effects of a new migraine medication. The initial level of pain was measured for each of 101 patients who suffer from migraine headaches and then each was randomly assigned to receive the treatment pill or a placebo pill. After two hours from consuming the pill, the level of pain is once again measured for each patient and the difference between the pain levels before and after taking the pills (i.e. before - after) is recorded. We are interested in determining if the new migraine medication is e'ective. Below is some R output: > tapply(PainDifference, Medicine, length) Placebo Treatment 50 51 > tapply(PainDifference, Medicine, mean) Placebo Treatment 0.400000 1.078431 > tapply(PainDifference, Medicine, sd) Placebo Treatment 0.9476071 0.9130857 > Model1 summary(Mode11) Residuals: Min 10 Median 30 Max 2.40000 0.40000 0.07843 0.60000 2.92157 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 0.4000 0.1316 3.040 0.003025 ** MedicineTreatment 0.6784 0.1852 3.664 0.000401 *** Residual standard error: 0.9303 on 99 degrees of freedom Multiple Rsquared: 0.1194, Adjusted Rsqnared: 0.1105 Fstatistic: 13.43 on 1 and 99 DF, p-value: 0.0004009 > anova(Mode11) Analysis of Variance Table Response: PainDifference Df Sum Sq Mean Sq P value Pr(>F) Medicine 1 11.621 11.620? 13.426 0.0004009 *** Residuals 99 85.686 0.8655 a) Write out the model that is being tted in Modell. Dene any variables you include. b) Test the question of interest using the above linear regression model. Your test should be in terms of one or more regression parameters; do not use the ANOVA Ftest. Include all the necessary steps for the hypothesis test. c) Test the question of interest using another method that is equivalent to the test done in part b). Include all the necessary steps for the hypothesis test. d) Explain Why the ANOVA Ftest (for the equality of the mean pain differences in the two medicine groups) cannot be directly used to test the question of interest