Within Arizona State, students were randomly assigned to one of two Mathematics teachers – Mrs. Elite and Mrs. Bright. After the assignment, Mrs. Elite had 30 students, and Mrs. Bright had 25 students. At the end of the year, each class took the same standardized test. Mrs. Elite’s students had an average test score of 78, with a standard deviation of 10; and Mrs. Bright’s students had an average test score of 85, with a standard deviation of 15.
Test the hypothesis that Mrs. Elite and Mrs. Bright are equally effective teachers. Use a 0.10 level of significance. (Assume that student performance is approximately normal.) (6mks)