Question

In a study designed to test the effectiveness of acupuncture for treating migraines, 142 subjects were treated with acupuncture and 80 subjects were given a sham treatment. The number of migraine attacks for the acupuncture treatment group had a mean of 1.8 and a standard deviation of 1.4. The number of migraine attacks for the sham treatment group had a mean of 1.6 standard deviation of 1.2.

A - construct the 95% confidence interval estimeate of mean number of migraine attacks for those treated with acupuncture and interpret finings.

B - test sham treatment is more effective than acupuncture treatment and interpret the findings a= 0.05

Answer 1

Answers: A) From theory,

Thus, the 95% confidence interval estimate of mean number of migraine attacks for those treated with acupuncture is given by--(1.57,2.03).

A 95% confidence interval is a range of values that you can be 95% certain contains the true mean of the population. Thus it can be interpreted as with 95% confidence it can be said that the true average number of migraine attacks for the acupuncture treatment group lies between (1.57 to 2.03).

B) In order to test if sham treatment is more effective than acupuncture treatment , we construct our null and alternative hypotheses as H0: mu1 = mu2 vs Ha: mu1 > mu2 where mu1 and mu2 are the number of migraine attacks for the acupuncture treatment group and sham treatment groups respectively

The test statistic used for this test is T= (x1bar-x2bar)/sqrt((s1*s1/n1)+(s2*s2/n2)) where x1bar, x2bar are the sample means, s1,s2 are the sample standard deviations and n1,n2 are the sample sizes. sqrt refers to the square root function.

We reject H0 if T(observed) > t(alpha,v) where t(alpha,v) is the upper alpha point of a Student's t distribution with "v" degrees of freedom. Alpha is the level of significance. v = (((s1*s1/n1)+(s2*s2/n2))^2) / (((s1*s1/n1)^2)/(n1-1))+(((s2*s2/n2)^2)/(n2-1))

Here T(observed) = 1.121495 and t(alpha,v) = 1.65311. (Obtained from the probability tables of Student's t distribution)

Thus we see that T(observed) < t(alpha,v). Thus we fail to reject H0 and conclude on the basis of the given sample at a 5% level of significance that there is not sufficient evidence to claim that sham treatment is more effective than acupuncture treatment.