A researcher from the Center for Equal Opportunity wants to determine if SAT scores of admitted students at a large state university differed by ethnicity. She collects data on SAT scores and ethnic background for 200 admitted students. A portion of the data is shown in the accompanying table. 

SAT                                                                 Ethnicity 

1515................................................................. White 

1530 .................................................................Latinx 

⋮................................................................................ ⋮ 

1614 ...................................................................White

a. Estimate the model y = β₀ + β₁d₁ + β₂d₂ + β₃d₃ + ɛ, where y represents a student’s SAT score; d₁ equals 1 if the student is white, 0 otherwise; d₂ equals 1 if the student is black, 0 otherwise; and d₃ equals 1 if the student is Asian, 0 otherwise. Note that the reference category is Latinx. What is the predicted SAT score for an Asian student? For a Latinx student? 

b. At the 5% significance level, determine if the SAT scores of Asian students differ from those of Latinx students. 

c. Reformulate the model to determine if the SAT scores of white students are lower than the SAT scores of Asian students at the 5% significance level. Your model must account for all ethnic categories.