The College Board provided comparisons of Scholastic Aptitude Test $($SAT$)$ scores based on the highest level of education attained by the test taker$$s parents. A research hypothesis was that students whose parents had attained a higher level of education would on average score higher on the SAT. The overall mean SAT math score was $514.$ SAT math scores for independent samples of students follow. The first sample shows the SAT math test scores for students whose parents are college graduates with a bachelor's degree. The second sample shows the SAT math test scores for students whose parents are high school graduates but do not have a college degree.

Student's Parents

College Grads High School Grads

$560560456552$

$672656444444$

$512512564444$

$576656396408$

$624624468408$

$576672444564$

$608560$

$528624$

a$.$ Formulate the hypotheses that can be used to determine whether the sample data support the hypothesis that students show a higher population mean math score on the SAT if their parents attained a higher level of education.