Question

A researcher is interested in whether participating in sports positively influences self-esteem in young girls. She identifies a group of girls who have not played sports before but are now planning to begin participating in organized sports. The researcher gives them a 50-item self-esteem inventory before they begin playing sports and administers the same test again after 6 months of playing sports. The self-esteem inventory is measured on an interval scale, with higher numbers indicating higher self-esteem. In addition, scores on the inventory are normally distributed. The scores follow. Before After 44 46 40 41 39 41 46 47 42 43 43 45 C. Conduct the appropriate analysis D. Should Ho be rejected? What should the researcher conclude?

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) = -1.5
We have d = -1.5
pooled variance = calculate value of Sd= √S^2 = sqrt [ 15-(-9^2/6 ] / 5 = 0.548
to = d/ (S/√n) = -6.708
critical Value
the value of |t α| with n-1 = 5 d.f is 2.571
we got |t o| = 6.708 & |t α| =2.571
make Decision
hence Value of | to | > | t α| and here we reject Ho
p-value :two tailed ( double the one tail ) - Ha : ( p != -6.7082 ) = 0.0011
hence value of p0.05 > 0.0011,here we reject Ho
ANSWERS
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C.
null, H0: Ud = 0
alternate, H1: Ud != 0
test statistic: -6.708
critical value: reject Ho, if to < -2.571 OR if to > 2.571
D.
decision: Reject Ho
p-value: 0.0011
we have enough evidence to support the claim that The self-esteem inventory is measured on an interval scale, with higher numbers indicating higher self-esteem.