Suppose that the 8 large regions of Vietnam were randomized into one of the following groups: in some regions, the local health care centers continued to be run by the government (control group: 4 regions) or in others, the health centers were subcontracted out to a NGO (treatment group: 4 regions). You have access to information from a child health survey, which covers 1,000 children per region and gives you information on whether or not the children have been fully immunized. A collaborator proposes to run a standard Neyman analysis, on the sample of 4,000 treatment and 4,000 control children, ignoring the region altogether. Denote YT=0.80 the sample average immunization rate in the treatment group, YC=0.58 the sample average immunization rate in the control group, σ2T=1.22 the estimated variance in the treatment group and σ2C=2.32 the estimated variance in the control group.

Required:
a. What is the collaborator's estimate of the average treatment effect?
b. What is the collaborator's estimate of the associated variance?