The file sesame contains data from an experiment in which a randomly selected group of children was encouraged to watch the television program Sesame Street and the randomly selected control group was not. The study took place in the United States and children of various demographics of interest were included. The settings studied included children from urban, suburban, and rural areas, both advantaged and disadvantaged children, and children from both English-speaking and Spanish-speaking households.

The dataset includes id (the subject id number), site (a categorical variable corresponding to the subject's demographic), age (in months), setting (recording whether the show was viewed 1=at home or 2=at school), pretest (the result of a test on letter recognition given before treatment assignment, with scores ranging from 0 to 58), encouraged (whether the subject was 0=not encouraged to watch, 1=encouraged to watch), and y (a post-test score from the same test on letter recognition).

The following prompts relate to the Sesame Street experiment and corresponding data.

(a) The goal of the experiment was to estimate the effect of watching more Sesame Street on child cognitive development. In the experiment, encouragement but not actual watching was randomized.

In one to three sentences, briefly explain why you think this was done. Give at least two (practical and/or statistical) reasons.

(b) Excluding any practical considerations about how easy/difficult it might be to conduct this experiment, list one benefit and one drawback of estimating causal effects in an encouragement design such as this.

(c) Suppose that instead of using a control group and randomized treatment assignment, the investigators had instead decided to test the effectiveness of the program simply by examining how test scores changed from before the intervention to after among those in the intervention arm.

In a single sentence, describe what assumption would be required for this to be an appropriate causal inference.

(d) Use data on just the control group from the study to evaluate just how realistic the assumption above would have been. In no more than three sentences, state whether or not you think the assumption is reasonable and why. In your justification, be sure to describe how the data support your conclusion.