You are helping the Ministry of Education in a low-income country to improve their investment decisions for educational attainment. The Ministry shares one large random sample of the population of primary schools from the past school year with you. Each school is one row of data, and you are able to observe the average student test score in each school from a national exam that all primary students in the country took at the end of the last school year (this variable is labeled TScore in the data). You are also able to observe other school characteristics that the Ministry has collected as additional variables in the dataset. A) The Ministry's first request is that you estimate the average of the school test score for the group of schools that received a federal grant to buy new school supplies, and also estimate how much that mean differed from the mean school test score of the group of schools that did not receive the federal grant. As part of the dataset, you observe the status of federal grant receipt in a dummy variable called FedGrant. Explain how you would use an OLS regression to obtain answers to these questions. Explain the interpretation of each of the point estimates. B) The Ministry also wants to know whether or not your estimated difference in the mean school test score between the two groups of schools is statistically significant, and at which level of statistical significance. Explain how you would use the results of the OLS regression in A) to answer this question. C) Your results in A) and B) suggest that the federal grant program decreased the average test score of schools. The head of staff criticizes your analysis, claiming you must have made an estimation mistake. As part of the dataset, you also observe the natural logarithm of the average household incomes of the students for each school. After you add this variable to the regression in A), the estimated sign of the grant program's effect switches. Explain what each point estimate of this regression captures, and explain to the head of staff what these results suggest concerning his criticism. Be as formal as possible in your explanation to her (using what we have learned about causal identification in OLS regressions). D) The Ministry is also interested in whether or not the federal grant program may have had different implications in the Southern school district of the country compared to the Northern school district. In your database, you observe a dummy variable North that indicates whether or not the school in question is located in the Northern school district (with 0 indicating it is in the Southern one). Explain how you would amend the OLS specification in A) to answer this question. Explain what each of the different coefficients would capture in your estimation