Assume that true proportions of the people who support "Obamacare" is a quarter of the population. If you took a sample of 1,000 people living in the United States, what would be the variance of this estimator?

what would be the expected value of your estimator for this proportion?

.25

To calculate the variance of the estimator for the proportion, we can use the formula for the variance of a proportion estimator, which is given by:

Var(p-hat) = (p * (1-p)) / n

Where:
- Var(p-hat) is the variance of the estimator for the proportion (p-hat)
- p is the true proportion (in this case, it is 0.25)
- (1 - p) is the complement of the true proportion
- n is the sample size (in this case, it is 1,000)

Let's calculate the variance:

Var(p-hat) = (0.25 * (1 - 0.25)) / 1000
= (0.25 * 0.75) / 1000
= 0.1875 / 1000
= 0.0001875

Therefore, the variance of this estimator for the proportion is approximately 0.0001875.

Now, let's calculate the expected value (mean) of the estimator for the proportion. The expected value is simply the true proportion itself, so the expected value of this estimator would be 0.25.

Therefore, the expected value of this estimator for the proportion is 0.25.