In 2000 a particular school district had a total of 7982 students enrolled in school. At this time, the percent of white students who were exposed to school poverty3 was 30% whereas this was 34.5% for Black students. The number of white students in this district in 2000 was 5184 and the number of Black students was 1035. (Note these are the deomgraphics for students who identify as one of these two races alone.) In 2015, the number of students enrolled in school in this district increased to 11977. The percent of white students exposed to school poverty increased to 47.8% and the percent for Black students increased to 76.1%. The number of white students in this district in 2015 was 7306 and the number of Black students was 2037.
Suppose we want to determine if, relative to the increased size of the school district from 2000 to 2015, is the difference between the proportion of white students exposed to poverty likely due to something besides chance. Perform an appropriate statistical hypothesis test at an α = 0.05 confidence level to answer this question. Show all your work and interpret your conclusion within the context of the problem and the appropriateness of the required assumptions.
Perform the same analysis as you did but this time to determine if there is statistical evidence of an actual difference between the proportion of Black students exposed to poverty.