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 158 patients diagnosed with migraine headaches were randomly assigned to one of two groups: treatment or control. 77 patients in the treatment group received acupuncture that is specifically designed to treat migraines. 81 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 = 0.1.

	Pain Free: Yes	Pain Free: No	Total
Treatment	20	57	77
Control	7	74	81
Total	27	131	158

a) What is the correct null hypothesis?

• H0H0: Migraine pain relief is independent on receiving acupuncture.
• H0H0: Migraine pain relief is dependent on receiving acupuncture.

b) Fill in the expected values, round answers to at least 2 decimal places.

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

c) Find the test statistic, round answer to 1 decimal place.
χ2χ2 =

d) What is the p-value? Round answer to at least 3 decimal places
P-value =

The p-value is...

• Greater than αα
• Less than αα

This P-Value leads to a decision to...

• Fail to reject the null hypothesis.
• Reject the null hypothesis.

e) What is the correct conclusion?

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

Answer 1

The statistical software output for this problem is :

H0: Migraine pain relief is independent on receiving acupuncture.

Test statistics = 8.4

P-value = 0.004

The p-value is Less than α

Reject the null hypothesis

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