An educator was interested in “cooperative play” versus “competitive play” activ

Question

An educator was interested in “cooperative play” versus “competitive play” activities as they might influence the ability of 5th grade students to make friends with their classmates. Specifically, the educator speculates that there will be a difference between the two conditions that will foster the acquisition of more friends, but the educator is not sure which way the difference will go. On a random basis, the educator divided a class of twenty 5th graders into two different styles of “play” activities at recess: a cooperative play group of ten children in which students relied on one another in order to get “team” recess activity points; and a competitive group of ten children in which students worked individually to outperform their classmates to get recess activity points. The data are presented below, and represent the number of classmates chosen by students as their friends at the end of the semester.

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Complete step 3 of the hypothesis testing procedure and calculate t using which ever formula you prefer. Round to the nearest hundredths place.

E. 3.51

F. NONE

Competitive Group
X1 Cooperative Group
X2 3 6 4 7 5 4 4 3 1 6 1 9 8 10 3 4 4 6 2

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Explanation / Answer

Given that,
mean(x)=3.5
standard deviation , s.d1=2.0683
number(n1)=10
y(mean)=6.4
standard deviation, s.d2 =2.3664
number(n2)=10
null, Ho: u1 = u2
alternate, H1: u1 != u2
level of significance, = 0.1
from standard normal table, two tailed t /2 =1.833
since our test is two-tailed
reject Ho, if to < -1.833 OR if to > 1.833
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =3.5-6.4/sqrt((4.27786/10)+(5.59985/10))
to =-2.92
| to | =2.92

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