7. MBB Problem 13.18 (modified): The Austin Independent School District wants to know whether the LBJ Magnet School for the Sciences is improving student performance. One hundred students were admitted as sophomores last year to the LBJ school. These students scored a mean of 14.7 on the junior year math achievement test (14 years, 7 months, or about a college sophomore level) with a standard deviation of 2.1. Twenty-three of these students play football. Education researcher Lana "Ein" Stein selects a control group of students who, in their sophomore year, performed comparably to the LBJ students in their sophomore year. These 144 students did not attend a magnet school. Their junior math achievement test produced a mean of 13.7 and a standard deviation of 2.9. Their mean IQ score was 117. Present a hypothesis, test this hypothesis, and present a conclusion in plain English regarding the magnet school students.