In: Math
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.
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 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. (Let μ1 = population mean verbal score
of students whose parents are college graduates with a bachelor's
degree and μ2 = population mean verbal score of students whose
parents are high school graduates but do not have a college
degree.)
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 for
the two populations?
(c)
Find the value of the test statistic. (Round your answer to three
decimal places.)
Compute the p-value for the hypothesis test. (Round your answer to
four decimal places.)
p-value =
(d)
At
α = 0.05,
what is your conclusion?
Do not Reject H0. There is sufficient evidence to conclude that
higher population mean verbal scores are associated with students
whose parents are college graduates.
Reject H0. There is sufficient evidence to conclude that higher
population mean verbal scores are associated with students whose
parents are college graduates.
Reject H0. There is insufficient evidence to conclude that higher
population mean verbal scores are associated with students whose
parents are college graduates.
Do not reject H0. There is insufficient evidence to conclude that
higher population mean verbal scores are associated with students
whose parents are college graduates.