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

469	503
550	549
666	526
554	426
534	515
572	594
497	432
608	485

High School Grads

442	492
580	478
479	425
486	485
528	390
524	535

c) find the value of the test statistic. (round your answer to three decimal places)

d) compute the p-value for the hypothesis test ( round your answer to four decimal places) p value=

Answer 1

Given that,
mean(x)=530
standard deviation , s.d1=63.255
number(n1)=16
y(mean)=487
standard deviation, s.d2 =51.7476
number(n2)=12
null, Ho: u1 = u2
alternate, H1: u1 != u2
level of significance, α = 0.05
from standard normal table, two tailed t α/2 =2.201
since our test is two-tailed
reject Ho, if to < -2.201 OR if to > 2.201
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =530-487/sqrt((4001.19503/16)+(2677.81411/12))
to =1.9767
| to | =1.9767
critical value
the value of |t α| with min (n1-1, n2-1) i.e 11 d.f is 2.201
we got |to| = 1.97667 & | t α | = 2.201
make decision
hence value of |to | < | t α | and here we do not reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != 1.9767 ) = 0.074
hence value of p0.05 < 0.074,here we do not reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: u1 != u2
c.
test statistic: 1.9767
critical value: -2.201 , 2.201
decision: do not reject Ho
d.
p-value: 0.074
we do not have enough evidence to support the claim that difference of means between
the SAT math test scores for students whose parents are college graduates with a bachelor's degree and
the SAT math test scores for students whose parents are high school graduates but do not have a college degree