Question 1 The disease Leprosy is an infection known to be caused by a rod-shaped bacterium called bacillus. Three types of treatments were administered to a sample of 10 patients per treatment group. The main aim of the research was to determine which type of treatment was effective in minimizing the bacillus score in the patients. It is known that the bacillus score after the treatment can be affected by the extent of the patients' pre-existing illness. We need to take into consideration the initial differences in the bacillus levels and examine how the final bacillus score vary between the treatments. The variables in the study are the initial score of the bacillus bacbef (x), bacafter (y) which is the bacillus score after and the treatment type. The data in question is in the Additional resources folder in the module site saved as "leprosyCSV". Download the data, import it into R software and answer the questions that follow. For all the tests of hypotheses, state all the relevant hypotheses, determine the critical (or rejection regions), report on the test statistics and give your conclusions. Present or attach the relevant R outputs used to answer your questions. 1. Motivate why ANCOVA is a plausible method of analysis that can be used to analyse these data. 2. Give a concise description of how ANCOVA differs from ANOVA. (4) 3. Explain three assumptions underlying an ANCOVA model. (6) 4. Plot the bacillus score after (y) against the initial bacillus score (x) while using different plotting symbols for the treatment type. Would you say that there appears to be a treatment type effect? (6) 5. Test, at five percent level of significance the null hypothesis that the covariate (bacillus score before) is not affected by the type of treatment. (8) 6. At the significance level of five percent, test whether the bacillus score before and the adjusted treatment type means are significant. (8) 7. Test the hypothesis of homogeneous regressions for each of the treatment types at 5% level of significance level. (8) 8. Write a one-way covariance model for the experiment and define what each term represents. (6) 9. Check the model of any violations of the assumptions by using relevant plots