Suppose You Want to Build a 90% Confidence Interval for the ATE

Suppose you want to build a 90% confidence interval for the ATE when the average outcome for the treated (55 subjects) is 12, with a sample standard deviation of 4, while the average outcome for the control (65 subjects) is 10, with a sample standard deviation of 6. Which of the following would be the proper confidence interval?

A) 0 ± 1.96 $\left( \sqrt { \frac { 4 ^ { 2 } } { 55 } + \frac { 6 ^ { 2 } } { 65 } } \right)$
B) 0 ± 1.65 $\left( \sqrt { \frac { 4 ^ { 2 } } { 55 } + \frac { 6 ^ { 2 } } { 65 } } \right)$
C) 2 ± 1.65 $\left( \sqrt { \frac { 4 ^ { 2 } } { 55 } + \frac { 6 ^ { 2 } } { 65 } } \right)$
D) 0 ± 1.96 $( \sqrt { ( 55 + 65 } )$