Question

Recall Karlan and List(2007) "Does Price Matter in Charitable Giving? Evidence from a Large-Scale Natural Field Experiment." In a new study, suppose that 10,000 previous donors are randomly and evenly divided into two separate groups. The "treatment group"receives a letter with a 2 to 1 match ratio. The "control group" receives a standard letter(no match). In the control group, 72 respond. In the treatment group, 91 respond. The point estimate of the difference in the response rate is 0.38 percentage points. What is the corresponding standard error(SE) of the difference?

Answer 1

Standard error is given by

Here,

First sample size is given by

Second sample size is given by

First sample proportion is given by

Second sample proportion is given by

Hence, corresponding standard error(SE) of the difference 0.002532533.