You may need to use the appropriate technology to answer thisquestion.
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 | 471 |
| 534 | 549 |
| 634 | 526 |
| 554 | 410 |
| 534 | 515 |
| 556 | 578 |
| 513 | 464 |
| 592 | 469 |
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 whetherthe sample data support the hypothesis that students show a higherpopulation mean math score on the SAT if their parents attained ahigher level of education. (Let ?1 = populationmean verbal score of students whose parents are college graduateswith a bachelor's degree and ?2 = populationmean verbal score of students whose parents are high schoolgraduates but do not have a college degree.) For purposes of thisstudy, assume the population variances are unequal when conductingthe t-test.
H0: ?1 ??2 < 0
Ha: ?1 ??2 = 0
H0: ?1 ??2 = 0
Ha: ?1 ??2 ? 0
H0: ?1 ??2 ? 0
Ha: ?1 ??2 = 0
H0: ?1 ??2 ? 0
Ha: ?1 ??2 < 0
H0: ?1 ??2 = 0
Ha: ?1 ??2 > 0
(b)
What is the point estimate of the difference between the meansfor the two populations?
(c)
Find the value of the test statistic. (Round your answer tothree decimal places.)
Compute the p-value for the hypothesis test. (Roundyour answer to four decimal places.)
p-value =
(d)
At
? = 0.05,
what is your conclusion?
Do not reject H0. There is insufficientevidence to conclude that higher population mean verbal scores areassociated with students whose parents are college graduates.Do notReject H0. There is sufficient evidence toconclude that higher population mean verbal scores are associatedwith students whose parents are collegegraduates. RejectH0. There is insufficient evidence to concludethat higher population mean verbal scores are associated withstudents whose parents are college graduates.RejectH0. There is sufficient evidence to concludethat higher population mean verbal scores are associated withstudents whose parents are college graduates.
