Assume that you are the lead researcher of a research project that seeks to understand the effects of providing the residents of a village with a new chlorine tablet that purifies water without producing any secondary effects. You receive enough funds to analyze the pill's effects using an RCT framework. Below is a table with the information your team has collected from 20 individuals. Those with numbers ID numbers 1 to 10 will receive the tablet treatment, while those with numbers 11 to 20 will not receive any tablets. ID Age Sex Income 0 1 25 113 27 1 35 28 0 40 25 1 112 26 0 28 1 24 23 25 26 24 25 1 26 0 23 1 0 23 4 5 6 7 8 9 10 11 12 13 14 15 25 16. 28 17 22 18 26 19 25 20 24 0 1 0 1 0 1 0 1 0 1 25 85 69 65 95 100 150 100 90 32 90 85 98 30 26 30 Table 1: Information about the intervention Years of education Health score before Health score after 6 5 7 8 4 5 9 5 5 9 5 8 7 6 8 10 8 664 7 6 7 5 5 01 1010 00101- 1054 2011.04.0 00 601-10 104 8 6 8 7 7 5 6 6 8 9 9 6 7 5 5 8 5 Each column has a different characteristic of the persons participating in the RCT of the new pill. For example, age refers to the age of the participants, sex to their sex, and is coded Male-0 and Female=1, and years of education refers to the years of schooling completed by the participant. The outcome variable of interest is a health score between zero (bad health) and 10 (excellent health). There are two moments of observation of this score. The first one, before the pill was distributed, is labeled as before. The second observation corresponds to the moment after the pill was distributed. With this information, answer the following questions: 1. Identify the treatment and control groups. 2. State what condition needs to hold for you to be able to estimate the average causal effect of the pill on the health score. 3. Estimate the sample mean for all variables except the health score after the intervention for both the treatment and control group. 4. State the hypothesis test necessary for the difference in means of each variable with the exception of the of the health score after the intervention. 5. Estimate the standard error of the difference in means between the treatment and the control group for each variable with the exception of the of the health score after the intervention. 6. Perform the hypothesis tests stated in question 4 for the 0.10, 0.05, 0.01 significance levels. 7. Based on the results from the previous questions, can you estimate the average causal effect of the pill as the difference in the mean health score after the intervention between the treatment and control groups? If so, estimate it. If it is not possible, explain why. 8. Is the average causal effect statistically different from zero? Perform the corresponding hypothesis test to answer this question.