A researcher is interested in whether there is a difference between two schools in students' aptitude for English. She randomly chooses 10 students from school \(X\) and 8 students of a similar age from school \(Y\) to take a written English test. The scores for the students from school \(X(x)\) and school \(Y(y)\) are summarised as follows.
\(\sum x=612 \quad \sum x^{2}=40104 \quad \sum y=444 \quad \sum y^{2}=27460\)

You should assume that the two distributions are normal and have the same population variance.
(a) Find a 95\% confidence interval for the difference in the mean scores for students from school \(X\) and students from school \(Y\) in the written English test.
(b) Use the confidence interval you found in part (a) to explain why there is insufficient evidence at a 5\% significance level to suggest that the English scores of students from school \(X\) and students from school \(Y\) are different.