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 High School
485 442
534 580
650 479
554 486
550 528
572 524
497 492
592 478
487 425
533 485
526 390
410 535
515
578
448
469

(a) Formulate the hypotheses that students show a higher population mean math score on the SAT if their parents attained a higher level of education.
(b) At Alpha=0.5, what is your conclusion?

Answer 1

Answer:

a. $H_{0}:$ u1≤u2

$H_{a} :u1>u2$

b P<0.05   rejected H

Step-by-step explanation:

College High School

485 442

534 580

650 479

554 486

550 528

572 524

497 492

592 478

487 425

533 485

526 390

410 535

515

578

448

469

The mean is the average . the sum of number over the number of observation

x1=525

x2=487

s.d1=59.42

s.d2=51.74

n1=16

n2=12$\alpha =0.05$

Determine the hypothesis

$H_{0}:$ u1≤u2

$H_{a} :u1>u2$

find the degree of freedom$(\frac{s1^2}{n1} +\frac{s2^2}{n2} )^2/(\frac{s1^2}{n1} )^2/n1-1+(s2^2/n2)^2/n2-1\\\\(\frac{59.42^2}{16} +\frac{51.7476^2}{12} )^2/(\frac{59.42^2}{16} )^2/16-1+(51.74^2/12)^2/12-1$

25

p-value is the probability of obtaining the value of the test statistics. In the column of t-value in the row df=25

0.025<P<0.05

if the P value is actually less than or the same as the significant level, then the null hypothesis is rejected

P<0.05   rejected H