A psychologist wants to know whether wives and husbands who both serve in a fore
ID: 3334208 • Letter: A
Question
A psychologist wants to know whether wives and husbands who both serve in a foreign war have similar levels of satisfaction in their marriage. To test this, six married couples currently serving in a foreign war were asked how satisfied they are with their spouse on a 7-point scale ranging from 1 (not satisfied at all) to 7 (very satisfied). The following are the responses from husband and wife pairs.
Married Couples
Wife Husband
6 4
2 5
6 4
6 5
6 4
5 4
(a) Test whether or not mean ratings differ at a 0.05 level of significance. State the value of the test statistic. (Round your answer to three decimal places.)
[Incorrect: Your answer is incorrect.]
State the decision to retain or reject the null hypothesis.
Retain the null hypothesis.Reject the null hypothesis. [Correct: Your answer is correct.]
(b) Compute effect size using eta-squared. (Round your answer to two decimal places.)
Explanation / Answer
a.
Given that,
mean(x)=5.1667
standard deviation , s.d1=1.6021
number(n1)=6
y(mean)=4.3333
standard deviation, s.d2 =0.5164
number(n2)=6
null, Ho: u1 = u2
alternate, H1: u1 != u2
level of significance, = 0.05
from standard normal table, two tailed t /2 =2.571
since our test is two-tailed
reject Ho, if to < -2.571 OR if to > 2.571
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =5.1667-4.3333/sqrt((2.56672/6)+(0.26667/6))
to =1.213
| to | =1.213
critical value
the value of |t | with min (n1-1, n2-1) i.e 5 d.f is 2.571
we got |to| = 1.21276 & | t | = 2.571
make decision
hence value of |to | < | t | and here we do not reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != 1.2128 ) = 0.279
hence value of p0.05 < 0.279,here we do not reject Ho
ANSWERS
---------------
test statistic: 1.213
b.
effective size ( eta squared = t^2 / t^2 + df = 1.213^2 / ( 1.213^2) + 5 = 0.22736
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