In this problem, you will use data from the 2018 Grade 10 Mathematics MCAS to investigate evidence

of achievement gaps in standardized test score at the school level. The mcas data contains

information on 355 schools in Massachusetts. Scores on the MCAS are classified into levels: warning/

failing, needs improvement, proficient, and advanced. Students who score in the "proficient"

category are said to "demonstrate a solid understanding of challenging subject matter", while

those in the "advanced" category are said to "demonstrate a comprehensive and in-depth understanding

of rigorous subject matter"; the variable PA_perc represents the percentage of students

at a school who score at the proficient or advanced level.

The descriptions of the variables are as follows.

Variable Description

PA_perc percentage of students scoring proficient or advanced

class_size average class size

math_class_size average math class size

student_teacher_ratio student to teacher ratio

attendance_rate average percentage of days attended across students

number_of_students total number of students who took the exam

largest_minority largest minority group among the student body

white_less50 coded TRUE if less than 50% of students are white

exp_per_pupil average expenditures per pupil in USD

econ_dis percentage of economically disadvantaged students

Some additional background on certain variables:

- Whether a student is economically disadvantaged is a proxy measure for student family

income; a student is considered economically disadvantaged if they are participating in one

or more of the following programs: the Supplemental Nutrition Assistance Program (SNAP),

the Transitional Assistance for Families with Dependent Children (TAFDC), the Department

of Children and Families' (DCF) foster care program, MassHealth (Medicaid).

- Expenditures per pupil is a proxy measure for the amount of funding available to a school

district. This variable is measured by district (i.e., constant for schools in the same district).

Use a modeling approach to estimate the association between the percentage of students

scoring at the proficient/advanced levels and whether a school's student body is less than

50% white, adjusting for the following potential confounders.

Add econ_dis to the model from part iii. and interpret the slope coefficient for

white_less50. Explain the difference in the interpretation of the slope coefficient for

white_less50 in this model versus the model from part iii., using terms accessible to

someone who has not taken a statistics course.