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.

Table 1: Information about the intervention 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