The following scores were obtained for the same subjects before and after a “psy

Question

The following scores were obtained for the same subjects before and after a “psychic abilities improvement” workshop. Higher scores on a test of “ESP” are interpreted as indication of increased levels of “psychic ability.*” You want to know if people who participate in this workshop will score higher on the test after completing the workshop. Do a 95% confidence interval. Then set alpha at .01 and test for a significant increase in ESP and calculate effect size if warranted. Please show ALL procedural steps. Participant

Participant Before After 1 5 7 2 5 7 3 4 4 4 3 4 5 7 8 6 3 4

Explanation / Answer

Confidence Interval
CI = d ± t a/2 * (Sd/ Sqrt(n))
Where,
d = di/n
Sd = Sqrt( di^2 – ( di )^2 / n ] / ( n-1 ) )
a = 1 - (Confidence Level/100)
ta/2 = t-table value
CI = Confidence Interval
d = ( di/n ) =-7/6=-1.167
Pooled Sd( Sd )= Sqrt [ 11- (-7^2/6 ] / 5 = 0.753
Confidence Interval = [ -1.167 ± t a/2 ( 0.435/ Sqrt ( 6) ) ]
= [ -1.167 - 2.571 * (0.307) , -1.167 + 2.571 * (0.307) ]
= [ -1.957 , -0.377 ]

HYPOTHESIS

Given that,
null, H0: Ud = 0
alternate, H1: Ud < 0
level of significance, = 0.01
from standard normal table,left tailed t /2 =3.365
since our test is left-tailed
reject Ho, if to < -3.365
we use Test Statistic  
to= d/ (S/n)
where
value of S^2 = [ di^2 – ( di )^2 / n ] / ( n-1 ) )
d = ( Xi-Yi)/n) = -1.167
We have d = -1.167
pooled variance = calculate value of Sd= S^2 = sqrt [ 11-(-7^2/6 ] / 5 = 0.753
to = d/ (S/n) = -3.797
critical Value
the value of |t | with n-1 = 5 d.f is 3.365
we got |t o| = 3.797 & |t | =3.365
make Decision
hence Value of | to | > | t | and here we reject Ho
p-value :left tail - Ha : ( p < -3.7974 ) = 0.00633
hence value of p0.01 > 0.00633,here we do not reject Ho
ANSWERS
---------------
null, H0: Ud = 0
alternate, H1: Ud < 0
test statistic: -3.797
critical value: reject Ho, if to < -3.365
decision: Reject Ho
p-value: 0.00633

have evidence that significance increase

cohen's d = Xd/ Sd = -7/ 0.753 = -9.296

X Y X-Y (X-Y)^2 5 7 -2 4 5 7 -2 4 4 4 0 0 3 4 -1 1 7 8 -1 1 3 4 -1 1 -7 11

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