Question

1) 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 164 patients diagnosed with migraine headaches were randomly assigned to one of two groups: treatment or control. 75 patients in the treatment group received acupuncture that is specifically designed to treat migraines. 89 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 = 0.01.

	Pain Free: Yes	Pain Free: No	Total
Treatment	17	58	75
Control	6	83	89
Total	23	141	164

a) What is the correct null hypothesis?

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

2)

6.36 Diabetes and unemployment: A 2012 Gallup poll surveyed Americans about their employment status and whether or not they have diabetes. The survey results indicate that 1.5% of the 47,774 employed (full or part time) and 2.5% of the 5,855 unemployed 18-29 year olds have diabetes.


(a) Create a two-way table presenting the results of this study.

	Diabetes	No Diabetes
Employed
Unemployed

(b) State appropriate hypotheses to test for independence of incidence of diabetes and employment status.

• H₀: Diabetes status and employment status are dependent
  H_a: Diabetes status and employment status are not dependent
• H₀: Diabetes status and employment status are independent
  H_a: Diabetes status and employment status are not independent
• H₀: μ_diabetes=μ_employed
  H_a: μ_diabetes ≠ μ_employed

(c) The sample difference is about 1%. If we completed the hypothesis test, we would find that the p-value is very small (about 0), meaning the difference is statistically significant. Use this result to explain the difference between statistically significant and practically significant findings.

• Since the sample sizes are so large and the difference between the two sample proportions is so small, we observe a statistically significant difference which may not be practically significant
• If our data don't provide strong enough evidence to reject the null hypothesis we should just collect more data until we can report the results that we want
• Being unemployed causes people to get diabetes at a higher rate

Answer 1