Question

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 High School Grads 485 471 442 492 550 549 sea 478 650 510 479 425 554 394 406 495 566 499 528 390 598 594 524 535 513 448 592 469 (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 - population mean math score of students whose parents are college graduates with a bachelor's degree and Y2 - population mean math score of students whose parents are high school graduates but do not have a college degree.) For purposes of this study, assume the population variances are unequal when conducting the t-test. Hou, - , 20 MM, -20 Ho: W.-20 Hou, - <0 4.4 -2 = 0 HIM - > 0 Ho: 4. - 2 = 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) Ata -0.05, what is your conclusion? Do not Reject Ho. There is sufficient evidence to conduce that higher population mean math scores are associated with students whose parents are college graduates. Do not reject. There is insufficient evidence to conclude the higher population mean math scores are associated with students whose parents are college graduates. Reject Hy. There is insufficient evidence to conclude that higher population mean math scores are associated with students whose parents are college graduates. Reject H, There is sufficient evidence to conclude that higher population mean math scores are associated with students whose parents are college graduates.

Answer 1

OSH D - Ýy = f("%.

b)

	College grads	High school Grads
sample mean x =	527.000	487.000
std deviation s=	65.468	51.748
sample size n=	16	12
std error se=s/√n=	16.367	14.938

Point estimate =x1-x2=

40.00

c)

test statistic t =(x1-x2-Δo)/Se=

1.805

degree freedom=(se12+se22)2/(se12/(n1-1)+se22/(n2-1))=

25

p value : =

0.0416

from excel: tdist(1.8051,25,1)

since p value<0.05

Reject Hg. There is sufficient evidence to conclude that higher population mean math soares are associated with students whose parents are college graduates.