Please help. I don\'t know how to do this. I might have the wrong answers. Pleas
ID: 3220446 • Letter: P
Question
Please help. I don't know how to do this. I might have the wrong answers. Please help me answer everything.
Average: 10 Attempts: 5. The t test for two independent samples Two-tailed example Aa Aa E "Bullying," according to noted expert Dan Olweus, "poisons the educational environment and affects the learning of every child." Bullying and victimization are evident as early as preschool with the problem peaking in middle school. Suppose you are interested in the emotional well-being of not only the victims but also bystanders, bullies, and those who bully but who are also victims (bully-victims). You decide to measure depression in a group of bullies and a group of bystanders using an 18-item, 5-point depression scale. Assume scores on the depression scale are normally distributed and that the variances of the depression scores are the same among bullies and bystanders. The group of 39 bullies scored an average of 51.6 with a sample standard deviation of 9 on the depression scale. The group of 31 bystanders scored an average of 45.2 with a sample standard deviation of 12 on the same scale. You do not have any presupposed assumptions about whether bullies or bystanders will be more depressed, so you formulate the null and alternative hypotheses as Ho: Hbullies Hbystanders 0 H1: Hbullies Hbystanders 0 You conduct an independent measures t test. Given your nu and alternative hypotheses, this is a two-tailed test. To use the Distributions tool to find the critical region, you first need to set the degrees of freedom. The degrees of freedom is 38 t Distribution Degrees of Freedom 78Explanation / Answer
Given that,
mean(x)=51.6
standard deviation , s.d1=9
number(n1)=39
y(mean)=45.2
standard deviation, s.d2 =12
number(n2)=31
null, Ho: u1 = u2
alternate, H1: u1 != u2
level of significance, = 0.05
from standard normal table, two tailed t /2 =1.995
since our test is two-tailed
reject Ho, if to < -1.995 OR if to > 1.995
calculate pooled variance s^2= (n1-1*s1^2 + n2-1*s2^2 )/(n1+n2-2)
s^2 = (38*81 + 30*144) / (70- 2 )
s^2 = 108.7941
we use test statistic (t) = (x-y)/sqrt(s^2(1/n1+1/n2))
to=51.6-45.2/sqrt((108.7941( 1 /39+ 1/31 ))
to=6.4/2.5098
to=2.55
| to | =2.55
critical value
the value of |t | with (n1+n2-2) i.e 68 d.f is 1.995
we got |to| = 2.55 & | t | = 1.995
make decision
hence value of | to | > | t | and here we reject Ho
p-value: two tailed ( double the one tail ) - ha : ( p != 2.55 ) = 0.013
hence value of p0.05 > 0.013,here we reject Ho
ANSWERS
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null, Ho: u1 = u2
alternate, H1: u1 != u2
test statistic: 2.55
critical value: -1.995 , 1.995
decision: reject Ho
p-value: 0.013