Question:

1. The following is obtained with the aid of R:
   
   The ATE is 1794.3.
   The corresponding standard error of the coefficient is
   \[se\left( {{{\hat{\beta }}}_{1}} \right)=632.9\]
   Therefore, the 95% confidence interval is given by
   \[CI=\left( {{{\hat{\beta }}}_{1}}-{{t}_{\alpha /2,n-p}}\times se\left( {{{\hat{\beta }}}_{1}} \right),\,{{{\hat{\beta }}}_{1}}+{{t}_{\alpha /2,n-p}}\times se\left( {{{\hat{\beta }}}_{1}} \right)\, \right)\]
   
   
   So the 95% CI for the ATE is .
2. Now we get the following with the aid of R:
   
   The regression-adjusted experimental estimate is 1670.7.
3. The following results are obtained with R:

The naïve estimate is -8506.5.

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