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# (Solved): 1. Given Assumption 1: Conditional Distribution Of Ui Given Xi Has Mean Zero: E[ui |Xi ] = 0 (a) Sup...

1. Given Assumption 1: Conditional distribution of ui given Xi has mean zero: E[ui |Xi ] = 0

(a) Suppose Xi and ui are independent and that E[ui ] = 0. Show that Assumption 1 holds.

(b) In the late 1980s, the Tennessee government ran project STAR. It cost \$12m to implement at the time (the Tennessee budget on K-12 education was \$212m in FY 2018-19). In project STAR, students and teachers were randomly assigned small (13-17 students) or large (22-25 students). Given data on 3733 students in the experiment, you wish to estimate Yi = Î²0 + Î²1Xi + ui where Yi is the test score for student i, and Xi = 1 if student i was in a small class and 0 if student i was in a large class. Explain why Assumption 1 holds in this setting.

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