A district-wide test is used to measure math aptitude in freshmen in high school students, with a mean of 78 and a standard deviation of 12. Thirty-six selected freshmen took the test, and their mean score was 85. You are tasked to examine if these students are significantly different from the district test group. 1. Calculate the standard error of the mean (SEM)?
2. After calculating the SEM, create a 95% confidence interval?