A composition teacher wishes to see whether a new grammar study program will reduce the number of grammatical errors her students make when writing a two$-$page essay. This data is normally distributed. The data from a sample of $6$ students are shown below.

$\backslash \backslash$table$[[$Student$,1,2,3,4,5,6],[\backslash \backslash$table$[[$Errors$],[$Before$]],12,9,0,5,4,3],[\backslash \backslash$table$[[$Errors$],[$After$]],9,6,1,3,2,3]]$

a$)$ What is the $95\%$ confidence interval for errors BEFORE the new program?