Use the following probabilities to answer the question. Round to 4 decimal places.

P(A)=0.37, P(B)=0.58, P(A and B)=0.05

P(B l A)=

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 89 females diagnosed with migraine headaches were randomly assigned to one of two groups: treatment or control. 43 patients in the treatment group received acupuncture that is specifically designed to treat migraines. 46 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 (Allais, 2011).
(round answers to 2 decimal places)

	Pain Free: Yes	Pain Free: No	Total
Treatment	10	33	43
Control	2	44	46
Total	12	77	89

a) What percent of patients in the treatment group were pain free 24 hours after receiving acupuncture? %
b) What percent of patients in the control group were pain free after 24 hours? %
c) At first glance, does acupuncture appear to be an effective treatment for migraines? Explain your reasoning.

no, because more than half of the individuals in the treatment group still experience pain 24 hours later

no, because there were fewer people in the treatment group

yes, because more individuals in the treatment group were pain-free after 24 hours

yes, because a higher percentage of individuals in the treatment group were pain-free after 24 hours

d) Do the data provide convincing evidence that there is a real pain reduction for those patients in the treatment group? Or do you think that the observed difference might just be due to chance?

Yes, 23% is much higher than 4%

It is impossible to tell merely by comparing the sample proportions because the difference could be the result of random error in our sample

Answer rating: 100% (QA)

a To find the percentage of patients in the treatment group who were painfree 24 hours after receivi... View the full answer