You must show all your work to receive credit. You may not use SPSS or Excel for

Question

You must show all your work to receive credit. You may not use SPSS or Excel for any of the problems on this exam. X *(10 points) A medical researcher is studying the effects of yoga exercise as relaxation treatment. Specifically, she is looking at the effect of the exercise on resting heart rate of individuals. She takes a group of 10 volunteers and measures their resting heart rates. Then, she has them enroll in a three-times-a-week yoga class for eight weeks. At the end of this period, she measures their resting h a eart the data are normal. Volunteer Reading 1 (before) 80 80 72 72 68 Reading 2 (after) 79 78 70 72 70 72 70 75 80 74 72 76 83 10

Explanation / Answer

Given that,
null, H0: Ud = 0
alternate, H1: Ud < 0
level of significance, = 0.05
from standard normal table,left tailed t /2 =1.833
since our test is left-tailed
reject Ho, if to < -1.833
we use Test Statistic  
to= d/ (S/n)
where
value of S^2 = [ di^2 – ( di )^2 / n ] / ( n-1 ) )
d = ( Xi-Yi)/n) = 1.4
We have d = 1.4
pooled variance = calculate value of Sd= S^2 = sqrt [ 40-(14^2/10 ] / 9 = 1.506
to = d/ (S/n) = 2.941
critical Value
the value of |t | with n-1 = 9 d.f is 1.833
we got |t o| = 2.941 & |t | =1.833
make Decision
hence Value of | to | > | t | and here we reject Ho
p-value :left tail - Ha : ( p < 2.9406 ) = 0.99176
hence value of p0.05 < 0.99176,here we reject Ho
ANSWERS
---------------
null, H0: Ud = 0
alternate, H1: Ud < 0
test statistic: 2.941
critical value: reject Ho, if to < -1.833
decision: Reject Ho
p-value: 0.99176
we have enough evidence to support yoga exercise leads to a decrese in resting heart rate

X Y X-Y (X-Y)^2 80 79 1 1 80 78 2 4 72 70 2 4 72 72 0 0 68 70 -2 4 74 72 2 4 72 70 2 4 76 75 1 1 83 80 3 9 77 74 3 9 14 40

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