Question

Migraine and Acupuncture: A migraine is a particularly painful type of headache, which patients sometimes wish to treat with acupuncture. To determine whether acupuncture relieves migraine pain, researchers conducted a randomized controlled study where 166 patients diagnosed with migraine headaches were randomly assigned to one of two groups: treatment or control. 67 patients in the treatment group received acupuncture that is specifically designed to treat migraines. 99 patients in the control group received placebo acupuncture (needle insertion at non-acupoint locations). 24 hours after patients received acupuncture, they were asked if they were pain free. Results are summarized in the contingency table below. Test to see if migraine pain relief is dependent on receiving acupuncture. Use αα = 0.05.

	Pain Free: Yes	Pain Free: No	Total
Treatment	16	51	67
Control	4	95	99
Total	20	146	166

a) What is the correct null hypothesis?

• H0H0: p1≠p2≠p3≠p4p1≠p2≠p3≠p4
• H0H0: p1=p2=p3=p4p1=p2=p3=p4
• H0H0: Migraine pain relief is dependent on receiving acupuncture.
• H0H0: Migraine pain relief is independent on receiving acupuncture.

b) Fill in the expected values, round answers to at least 4 decimal places.

Expected Values	Pain Free: Yes	Pain Free: No
Treatment
Control

Answers show on last attempt	Pain Free: Yes	Pain Free: No
Treatment
Control

c) Find the test statistic, round answer to at least 4 decimal places.

d) What is the p-value?

e) What is the correct conclusion?

• There is no statistical evidence that migraine pain relief is dependent on receiving acupuncture.
• There is statistical evidence that migraine pain relief is dependent on receiving acupuncture.

Answer 1

(a)

Correct option:

H0: Migraine pain relief is independent on receiving acupuncture.

(b)

Expected Values:

Expected Values	Pain free: Yes	Pain free: No	Total
Treatment	(20X67)/166 = 8.0723	(146X67)/166 = 58.9277	67
Control	(20X99)/166 = 11.9277	(146X99)/166 = 87.0723	99
Total	20	146	166

So,

Answer is:

Expected Values:

Answers show on last attempt	Pain free: Yes	Pain free: No	Total
Treatment	8.0723	58.9277	67
Control	11.9277	87.0723	99
Total	20	146	166

(c)

The Test Statistic is got as follows:

Observed (O)	Expected (E)	(O - E)2/E
16	8.0723	7.7857
51	58.9277	1.0665
4	11.9277	5.2691
95	87.0723	0.7218
Total = =		14.8432

So,

The Test Statistic = 14.8432

(d)

ndf = (r - 1) X (c - 1)

= (2 - 1) X (2 - 1)

= 1

By Technology, p - value = 0.0001

(e)

Correct option:

There is statistical evidence that migraine pain relief is dependent on receiving acupuncture.