It was thought that hypnosis would lower a person\'s desire to smoke. A research

Question

It was thought that hypnosis would lower a person's desire to smoke. A researcher decided to investigate this hypothesis using a paired-sample sign test in which the number of cigarettes/day smoked by subjects was recorded before and after hypnosis. Given that the critical value at = 0.05 in a one-tailed test is 1, is there enough evidence to support the hypothesis? Subject 1 2 3 4 5 6 7 8 9 10 Before Hypnosis (Cigarettes/day) 18 20 25 15 19 21 30 16 13 20 After Hypnosis (Cigarettes/day) 16 18 24 10 20 23 26 15 14 18 Since the critical value is less than the test value, there is not enough evidence to reject the null hypothesis. Consequently, the data do not support the hypothesis that hypnosis reduces smoking. Since the critical value is greater than the test value, there is not enough evidence to reject the null hypothesis. Consequently, the data do not support the hypothesis that hypnosis reduces smoking. Since the critical value is less than the test value, there is enough evidence to reject the null hypothesis. Consequently, the data support the hypothesis that hypnosis reduces smoking. Since the critical value is greater than the test value, there is enough evidence to reject the null hypothesis. Consequently, the data support the hypothesis that hypnosis reduces smoking.

Explanation / Answer

Given that,
null, H0: Ud = 0
alternate, H1: Ud < 0
level of significance, = 0.05
from standard normal table,right tailed t /2 =1.833
since our test is right-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) = 1.3
We have d = 1.3
pooled variance = calculate value of Sd= S^2 = sqrt [ 61-(13^2/10 ] / 9 = 2.21
to = d/ (S/n) = 1.86
critical Value
the value of |t | with n-1 = 9 d.f is 1.833
we got |t o| = 1.86 & |t | =1.833
make Decision
hence Value of | to | > | t | and here we reject Ho
p-value :right tail - Ha : ( p > 1.8571 ) = 0.04813
hence value of p0.05 > 0.04813,here we reject Ho
ANSWERS
---------------
null, H0: Ud = 0
alternate, H1: Ud < 0
test statistic: 1.86
critical value: reject Ho, if to > 1.833
decision: Reject Ho
p-value: 0.04813
the critical value is greater than the test value, there is enough evidence to reject the null hypothesis. Consequently, the data support the hypothesis that hypnosis reduces smoking

X Y X-Y (X-Y)^2 18 16 2 4 20 18 2 4 25 24 1 1 15 10 5 25 19 20 -1 1 21 23 -2 4 30 26 4 16 16 15 1 1 13 14 -1 1 20 18 2 4 13 61

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