additional covariate to the regression estimating the effect of the mailers on turnout in August 2006 you ran in part d)? Why or why not? [3 points] h. Imagine you were interested in the effect of sending these mailers in July 2006 on voter turnout in November 2006 and so ran a regression with November 2006 turnout as the outcome. Would you add voter turnout in August 2006 to this regression? Why or why not? [3 points] Problem 4. - Statistical Power, Blocking, Clustering [8 points] In planning an impact measurement, one important question is whether the measurement will have sufficient statistical power to be informative. As a corollary, as someone trained in how to measure impact, you should be ready to notice aspects of an impact measurement that will decrease statistical power. and be able to spot potential strategies for increasing statistical power. This will allow you to avoid drawing erroneous conclusions and wasting time -- or to learn much more than you originally thought possible. In this question, we will think through the intuition behind statistical power and how sample size, blocking, and clustering relate to power. As a reminder, statistical power refers to the probability of rejecting the null hypothesis in the presence of a true treatment effect. Part a [4 points] Suppose you want to evaluate the impact of a new team performance management system at your company, the "OKR" system used by Google, Uber, Linkedln and others. To track the impact of this system, you will measure individual-level employee outcomes, such as the number of hours employees spend working, theirjob satisfaction, and other such metrics. The lead of your data science team has prepared an experiment: managers together with their entire teams of employees will be randomly assigned to either use the OKR system or not over the next quarter. The data science lead has said, given that you have 1,000 employees, the experiment will be sufficiently well-powered. However, you know that you only have 50 managersfteams at your company, and that entire managersfteams always need to be in the same group (e.g., it's not possible for half ofa manager's team to the in the treatment group and for half to not). State whether this is an example of clustering or blocking and explain its effect on the statistical power in plain language. Part b [4 points] Suppose we want to evaluate the impact of a new drug your pharmaceutical company has developed on whether someone is cured of a rare disease. Previous data has told you that women are much more likely to recover from this rare disease of their own accord than are men, only a few of whom are able to fight the disease naturally. Could blocking or clustering be used to increase the power of this experiment? It so, how would you implement it