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 160 patients diagnosed with migraine headaches were randomly assigned to one of two groups: treatment or control. 72 patients in the treatment group received acupuncture that is specifically designed to treat migraines. 88 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 \\( \alpha = 0.1 \\).

	pain free: yes	pain free: no	total
control	8	80	88
total	22	138	160

a) what is the correct null hypothesis?

\\( \bigcirc h_0 \\): migraine pain relief is dependent on receiving acupuncture.
\\( \bigcirc h_0 \\): migraine pain relief is independent on receiving acupuncture.
\\( \bigcirc h_0 \\): \\( p_1 = p_2 = p_3 = p_4 \\)
\\( \bigcirc h_0 \\): \\( p_1 \
eq p_2 \
eq p_3 \
eq p_4 \\)

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

expected values	pain free: yes	pain free: no
control

Explanation:

Step1: Identify null hypothesis

Null hypothesis for independence test states no dependence.

Step2: Calculate expected values

Expected value = (row total × column total) / grand total.

For Treatment-Yes:

$(72×22)/160 = 1584/160 = 9.9$

For Treatment-No:

$(72×138)/160 = 9936/160 = 62.1$

For Control-Yes:

$(88×22)/160 = 1936/160 = 12.1$

For Control-No:

$(88×138)/160 = 12144/160 = 75.9$

Answer:

a) H₀: Migraine pain relief is independent on receiving acupuncture.
b)

Expected Values	Pain Free: Yes	Pain Free: No
Control	12.1000	75.9000