I have a data set of 412 schools and the mean SAT scores for these schools in 2012. I have created a dummy variable called high-income and low-income school based on the number of students that receive free or reduced lunches.
I want to conduct a Hypothesis tests for the difference of two means where I hope to set up the following hypothesis
H0-There is no average difference in SAT score between low-income and high income schools
HA- There is a difference in mean SAT scores between the low-income and high income schools.
I'm not sure if I have fulfilled the assumptions to carry out a difference of two means t-test
There are 1700 schools in NYC, and the dataset I have has 412 schools. However I am not sure if this data comes from an independent random samples. Also within these 412 schools only 142 schools fall as "high-poverty" and "low-poverty" category.
In such a situation should I not conduct the hypothesis test I have proposed