Question

an aura - Migraines (recurrent headaches that are moderate to severe) can be accompanied by a range of symptoms, one of which is a series of sensory disturbances, often characterized by flashes of light, blind spots, or a tingling sensation in the face or hands. Researchers gave a new medication to a random selection of 6 migraine patients and the length of symptoms (measured in minutes) was recorded for an attack before the medication (ui) and for an attack after the medication (u2). The results appear below: 1 2 3 4. 5 6 Patient Before medication After medication 76 93 45 129 58 81 52 87 64 91 47 75 Calculate the value of the test statistic the researchers would use to test their claim that the new medication reduces the average length of migraines with aura symptoms. If needed, you may assume that the length of symptoms both before and after being given the medication follows a normal distribution. Give your answer accurate to 3 decimal places. Answer:

Answer 1

Given that,
null, H0: Ud = 0
alternate, H1: Ud < 0
level of significance, α = 0.05
from standard normal table,left tailed t α/2 =2.015
since our test is left-tailed
reject Ho, if to < -2.015
we use Test Statistic
to= d/ (S/√n)
where
value of S^2 = [ ∑ di^2 – ( ∑ di )^2 / n ] / ( n-1 ) )
d = ( Xi-Yi)/n) = 11
We have d = 11
pooled variance = calculate value of Sd= √S^2 = sqrt [ 2574-(66^2/6 ] / 5 = 19.225
to = d/ (S/√n) = 1.402
critical Value
the value of |t α| with n-1 = 5 d.f is 2.015
we got |t o| = 1.402 & |t α| =2.015
make Decision
hence Value of |to | < | t α | and here we do not reject Ho
p-value :left tail - Ha : ( p < 1.4015 ) = 0.89001
hence value of p0.05 < 0.89001,here we do not reject Ho
ANSWERS
---------------
null, H0: Ud = 0
alternate, H1: Ud < 0
test statistic: 1.402
critical value: reject Ho, if to < -2.015
decision: Do not Reject Ho
p-value: 0.89001
we do not have enough evidence to support the claim that the new medication reduces the average length of migrains with aura symptoms.