In the Context of a Controlled Experiment, Consider the Simple $Y _ { i } = \beta _ { 0 } + \beta _ { 1 } X _ { i } + u _ { i } \text {. Let the } Y _ {i}$

question 14

Multiple Choice

In the context of a controlled experiment, consider the simple linear regression formulation $Y _ { i } = \beta _ { 0 } + \beta _ { 1 } X _ { i } + u _ { i } \text {. Let the } Y _ {i}$ be the outcome, $X _ { \mathrm { i } }$ the treatment level, and $u _ { i }$ contain all the additional determinants of the outcome. Then

• A) the OLS estimator of the slope will be inconsistent in the case of a randomly assigned \(X _ { i }\) since there are omitted variables present.
• B) \(X _ { \mathrm { j } } \text { and } u _ { \mathrm { i } }\) will be independently distributed if the \(X _ { \mathrm { i } }\) be are randomly assigned.
• C) \(\beta _ { 0 }\) represents the causal effect of X on Y when X is zero.
• D) \(E ( Y \mid X = 0 )\) is the expected value for the treatment group.

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Definitions:

Z-score

A statistical measure that describes a value's relationship to the mean of a group of values, expressed in terms of standard deviations from the mean.

Sampling Distribution

The sampling distribution is a probability distribution of a statistic obtained by selecting all possible samples of a specific size from a population.

Sampling Distribution

A probability distribution of a statistic obtained from a large number of samples drawn from a specific population.

Mean

The average of a set of numbers, calculated by dividing the sum of all the values by the number of values.