4. Bibliotherapy is a common tool to use with children who have a hard time bond

Question

4. Bibliotherapy is a common tool to use with children who have a hard time bonding with a therapist and opening up during therapy sessions. Dr. Contos wants to examine if children who participate in bibliotherapy (M=16.48, SD=2.67) score lower on levels of anxiety (0-25) than children who participate in play therapy (M=18.11, SD=2.58). She interviews 25 children in each group for a total of 50 children.

A. What are the independent and dependent variables and how are each scaled ?

            Independent:________________________            Scaling:_____________________________

            Dependent:__________________________            Scaling:_____________________________

B. What test should the students use?

E. What are that tests assumptions?  

H. If Audi calculates a test statistic of 4.76, should they?      Retain H0 Reject H0  

Explanation / Answer

4.
A.
An independent variable, sometimes called an experimental or predictor variable.
it is a variable that is being manipulated in an experiment in order to observe the effect on a dependent variable,
sometimes called an outcome variable.
independent variable : children who participate in bibliotherapy
dependent variable : children who participate in play therapy

B.
Z test for difference of mean
Given that,
mean(x)=16.48
standard deviation , 1 =2.67
number(n1)=25
y(mean)=18.11
standard deviation, 2 =2.58
number(n2)=25
null, Ho: u1 = u2
alternate, H1: 1 < u2
level of significance, = 0.05
from standard normal table,left tailed z /2 =1.645
since our test is left-tailed
reject Ho, if zo < -1.645
we use test statistic (z) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
zo=16.48-18.11/sqrt((7.1289/25)+(6.6564/25))
zo =-2.195
| zo | =2.195
critical value
the value of |z | at los 0.05% is 1.645
we got |zo | =2.195 & | z | =1.645
make decision
hence value of | zo | > | z | and here we reject Ho
p-value: left tail - Ha : ( p < -2.195 ) = 0.01408
hence value of p0.05 > 0.01408,here we reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: 1 < u2
test statistic: -2.195
critical value: -1.645
decision: reject Ho
p-value: 0.01408

E.
Assumption,level of significance, = 0.05
H.
no,test statistic is different we get
we have enough evidence the claim that children who participate in bibliotherapy score lower on levels of anxiety than children who participate in play therapy

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