Now assume that Data Set A depicts the scores of five subjects who received both

Question

Now assume that Data Set A depicts the scores of five subjects who received both Treatment 1 and Treatment 2. Calculate a t-test for dependent means to determine whether the means for the two treatments were significantly different. The correlation between the two treatments is +1.00. In your complete answer, remember to include your t-statistic, hypothesis. For this quetion, you should assume that the same participants received each of the two treatments. (10 points) critical v e, and your decision about whether to reject the null

Explanation / Answer

Given that,
null, H0: Ud = 0
alternate, H1: Ud != 0
level of significance, = 0.05
from standard normal table, two tailed t /2 =2.776
since our test is two-tailed
reject Ho, if to < -2.776 OR if to > 2.776
we use Test Statistic  
to= d/ (S/n)
where
value of S^2 = [ di^2 – ( di )^2 / n ] / ( n-1 ) )
d = ( Xi-Yi)/n) = -25
We have d = -25
pooled variance = calculate value of Sd= S^2 = sqrt [ 3375-(-125^2/5 ] / 4 = 7.91
to = d/ (S/n) = -7.07
critical Value
the value of |t | with n-1 = 4 d.f is 2.776
we got |t o| = 7.07 & |t | =2.776
make Decision
hence Value of | to | > | t | and here we reject Ho
p-value :two tailed ( double the one tail ) - Ha : ( p != -7.0711 ) = 0.0021
hence value of p0.05 > 0.0021,here we do not reject Ho
ANSWERS
---------------
null, H0: Ud = 0
alternate, H1: Ud != 0
test statistic: -7.07
critical value: reject Ho, if to < -2.776 OR if to > 2.776
decision: Reject Ho
p-value: 0.0021

X Y X-Y (X-Y)^2 45 60 -15 225 50 70 -20 400 55 80 -25 625 60 90 -30 900 65 100 -35 1225 -125 3375

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