A researcher conducted an experiment to test the effectiveness of a new drug on a viral infection. The infection was induced in a total of 200 mice, which were then randomly divided into two groups. Mice in Group A were treated with the new drug while mice in Group B were not. After a period of 14 days, the following results were obtained.

 Group A Group B Sample size: 100 100 Number of mice free of infection: 84 60 

a). Find the corresponding P-Value to test the hypotheses Ho: Pa =Pb against H1: Pa not equal Pb, where Pa and Pb are the proportions of mice free of infection after being treated with the new drug and not treated, respectively. Interpret your answer.

b). Student in a particular statistics course were randomly divided into four groups and each group was taught using a different teaching method. A lecturer is interested to know if there is any difference between the four teaching methods based on the scores of the students for the course. Assume that the scores of the students are normally distributed for each of the teaching methods. Random samples were drawn from the students following each teaching method and their scores for the course are recorded as follows.

 Method 1 Method 2 Method 3 Method 4 85 54 63 47 23 17 13 53 45 38 25 68 66 53 31 79 75 58 53 89 76 64 63 93 80 70 79 

i). Using the R software or otherwise, plot side-by-side boxplots for the scores of the students for all four teaching methods. Describe the plot in terms of the central tendency and dispersion of the scores.

ii). At the 0.10 level of significance, test the null hypothesis that the mean score for each of the four teaching methods is the same. State the null and alternative hypotheses, and define all notations used clearly.

iii). Suppose that the lecturer rejected the null hypothesis after running a hypothesis testing. Suggest how the lecturer can identify which teaching methods yield mean scores that are significantly different.