The College Board provided comparisons of Scholastic AptitudeTest (SAT) scores based on the highest level of education attainedby the test taker's parents. A research hypothesis was thatstudents whose parents had attained a higher level of educationwould on average score higher on the SAT. The overall mean SAT mathscore was 514. SAT math scores for independent samples of studentsfollow. The first sample shows the SAT math test scores forstudents whose parents are college graduates with a bachelor'sdegree. The second sample shows the SAT math test scores forstudents whose parents are high school graduates but do not have acollege degree.
College Grads
501   487
534   533
666   510
554   394
566   531
556   594
481   464
608   485

High School Grads
442   492
580   478
479   425
486   485
528   390
524   535
(a)
Formulate the hypotheses that can be used to determine whether thesample data support the hypothesis that students show a higherpopulation mean math score on the SAT if their parents attained ahigher level of education. (Let μ1 = population mean verbal scoreof students whose parents are college graduates with a bachelor'sdegree and μ2 = population mean verbal score of students whoseparents are high school graduates but do not have a collegedegree.)

H0: μ1 − μ2 = 0
Ha: μ1 − μ2 ≠ 0

H0: μ1 − μ2 < 0
Ha: μ1 − μ2 = 0
  

H0: μ1 − μ2 ≠ 0
Ha: μ1 − μ2 = 0

H0: μ1 − μ2 ≥ 0
Ha: μ1 − μ2 < 0

H0: μ1 − μ2 ≤ 0
Ha: μ1 − μ2 > 0
(b)
What is the point estimate of the difference between the means forthe two populations?

(c)
Find the value of the test statistic. (Round your answer to threedecimal places.)

Compute the p-value for the hypothesis test. (Round your answer tofour decimal places.)
p-value =
(d)
At
α = 0.05,
what is your conclusion?
Do not Reject H0. There is sufficient evidence to conclude thathigher population mean verbal scores are associated with studentswhose parents are college graduates.
Reject H0. There is sufficient evidence to conclude that higherpopulation mean verbal scores are associated with students whoseparents are college graduates.
Reject H0. There is insufficient evidence to conclude that higherpopulation mean verbal scores are associated with students whoseparents are college graduates.
Do not reject H0. There is insufficient evidence to conclude thathigher population mean verbal scores are associated with studentswhose parents are college graduates.