(Solved): The College Board provided comparisons of Scholastic Aptitude Test (SAT) scores bssed on the highes ...

The College Board provided comparisons of Scholastic Aptitude Test (SAT) scores bssed on the highest lovel of education attained by the test taker's perents. A research hypothesis was that students whose parents had attained a higher level of education would on avarage 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 5 AT math test scores for students whose parents are. high school graduates but do not have a college degree. a. Formulate the hypotheses that can be used to determine whether the sample datn support the hypothesis thot students show a higher populatisn mean math score on the SAT if their parents attained a higher level of education. \( \mu_{1}= \) pepulation mean verbal scort parents college gradt. \( \mathrm{A}_{2}= \) pooulation mean verbal score parents high school grads. \[ \begin{array}{l|l} H_{0}: \mu_{1}-\mu_{2} & 0 \\ H_{4}: \mu_{1}-\mu_{2} \end{array} \] b. What is the point estimate of the difference between the means for the two populations? (to I decimal) points if parents are college grads. c. Compute the pivalue for the hypothesis test. \( t \)-value G) (to 3 decimals) Degrees of freedom (round your answer to next whole number) \( p \)-value is d. At \( \alpha=0.05 \), what is your conclusien?