Question

(12 pts) The Inventory of Parent and Peer Attachment measures the level of attachment of individuals to their friends. A higher score indicates greater attachment. An education researcher wonders if there is a difference in the IPPA mean scores of students who participate in community service and those that do not. She surveyed 57 students who had done service work and 17 who had not. The sample mean IPPA scores and standard deviations are tabled below. Group Condition n ?̅ s 1 Service 57 104.12 14.68 2 No service 17 96.82 14.26 Does the survey data give significant evidence of a difference in the mean IPPA scores for students in the two community service groups? Address this question with the appropriate procedure. Give all the details.

Answer 1

Given that,
mean(x)=104.12
standard deviation , s.d1=14.68
number(n1)=57
y(mean)=96.82
standard deviation, s.d2 =14.26
number(n2)=17
null, Ho: u1 = u2
alternate, H1: u1 != u2
level of significance, α = 0.05
from standard normal table, two tailed t α/2 =2.12
since our test is two-tailed
reject Ho, if to < -2.12 OR if to > 2.12
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =104.12-96.82/sqrt((215.5024/57)+(203.3476/17))
to =1.84
| to | =1.84
critical value
the value of |t α| with min (n1-1, n2-1) i.e 16 d.f is 2.12
we got |to| = 1.83987 & | t α | = 2.12
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 != 1.8399 ) = 0.084
hence value of p0.05 < 0.084,here we do not reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: u1 != u2
test statistic: 1.84
critical value: -2.12 , 2.12
decision: do not reject Ho
p-value: 0.084
we do not have enough evidence to support the claim that difference in the mean IPPA scores for students in the two community service groups.