Question

A health psychologist tests a new intervention to determine if it can change healthy behaviors among siblings. To conduct the this test using a matched-pairs design, the researcher gives one sibling an intervention, and the other sibling is given a control task without the intervention. The number of healthy behaviors observed in the siblings during a 5-minute observation were then recorded.

Intervention
Yes	No
6	4
3	5
6	4
6	5
6	4
5	4

(a) Test whether or not the number of healthy behaviors differ at a 0.05 level of significance. State the value of the test statistic. (Round your answer to three decimal places.)


State the decision to retain or reject the null hypothesis.

Retain the null hypothesis.Reject the null hypothesis.    

(b) Compute effect size using eta-squared. (Round your answer to two decimal places.)

Answer 1

Given that,
null, H0: Ud = 0
alternate, H1: Ud != 0
level of significance, α = 0.05
from standard normal table, two tailed t α/2 =2.571
since our test is two-tailed
reject Ho, if to < -2.571 OR if to > 2.571
we use Test Statistic
to= d/ (S/√n)
where
value of S^2 = [ ∑ di^2 – ( ∑ di )^2 / n ] / ( n-1 ) )
d = ( Xi-Yi)/n) = 1
We have d = 1
pooled variance = calculate value of Sd= √S^2 = sqrt [ 18-(6^2/6 ] / 5 = 1.549
to = d/ (S/√n) = 1.581
critical Value
the value of |t α| with n-1 = 5 d.f is 2.571
we got |t o| = 1.581 & |t α| =2.571
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 != 1.5811 ) = 0.1747
hence value of p0.05 < 0.1747,here we do not reject Ho
ANSWERS
---------------
a.
null, H0: Ud = 0
alternate, H1: Ud != 0
test statistic: 1.581
critical value: reject Ho, if to < -2.571 OR if to > 2.571
decision: Do not Reject Ho
p-value: 0.1747
we do not have enough evidence to support the claim that whether or not the number of healthy behaviors differ at a 0.05 level of significance.
b.
effect size = d = ( Xi-Yi)/n) /S.D pooled
S^2 = sqrt [ 18-(6^2/6 ] / 5 = 1.549
S.D pooled = sqrt (1.549) = 1.2445
effect size = d/S.D pooled
effect size = 1/1.2445
effect size = 0.8035
large effect