Questions 1- 5 are based on the same scenario Consider the following hypothetical dataset

Consider the following hypothetical dataset:

Q1a. For the 8 units in the experiment, suppose we were to conduct a Bernoulli experiment with, for every unit, a propensity score of .5 of treatment.

ii. What is the probability we get an assignment where all units receive treatment or do not receive treatment? Round answer to two significant figures.

Consider the following hypothetical dataset:

Q1a. For the 8 units in the experiment, suppose we were to conduct a Bernoulli experiment with, for every unit, a propensity score of .5 of treatment.

iii. What is the probability we get an assignment where 1/2 the units receive treatment and 1/2 do not? Round your answer to the nearest hundredth.

Consider the following hypothetical dataset:

Q1a. For the 8 units in the experiment, suppose we were to conduct a Bernoulli experiment with, for every unit, a propensity score of .5 of treatment.

iv. What is the probability we get an assignment where 4 units are treated and 2 women and 2 men receive treatment? Round your answer to the nearest hundredth.

Consider the following hypothetical dataset:

Q1a. For the 8 units in the experiment, suppose we were to conduct a Bernoulli experiment with, for every unit, a propensity score of .5 of treatment.

v. What is the probability we get an assignment where all the women either receive treatment or do not receive treatment? Round your answer to the nearest hundredth.

Q1b. Now suppose we had conducted a completely randomized experiment. Clearly we no longer can end up with the situation where all units receive the same treatment. Also all assignment have half the subjects treated, half not.

ii. What is the probability of getting an assignment where 2 women and 2 men receive treatment? Round your answer to two significant figures.

Q1b. Now suppose we had conducted a completely randomized experiment. Clearly we no longer can end up with the situation where all units receive the same treatment. Also all assignment have half the subjects treated, half not.

iii. What is the probability we get an assignment where all the women either receive treatment or do not receive treatment? Round your answer to two significant figures.

Q1c. Now suppose we have conducted a randomized block experiment, with two blocks, one for men, one for women. Within each block 2 subjects are treated. Clearly, every assignment will feature 2 men and 2 women receiving treatment. How many elements are in Ω and what is the probability of any given assignment?

Q1d. Now suppose we have matched each women with another woman, and each man with another man, giving us 4 matched pairs. In this paired randomized experiment, what is Ω and how many elements are in Ω.