Question 1132964: 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).
(please round answers to within one hundredth of a percent)
Pain Free: Yes No Total
Treatment 10 33 43
Control 2 44 46
Total 12 77 89
1) What percent of patients in the treatment group were pain free 24 hours after receiving acupuncture? ________%
2) What percent of patients in the control group were pain free after 24 hours?
_________ %
3) Multiple Choice: At first glance, does acupuncture appear to be an effective treatment for migraines? Explain your reasoning.
(a) no, because there were fewer people in the treatment group
(b) yes, because more individuals in the treatment group were pain-free after 24 hours
(c) no, because more than half of the individuals in the treatment group still experience pain 24 hours later
(d) yes, because a higher percentage of individuals in the treatment group were pain-free after 24 hours
4) Multiple choice: 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?
(a) Yes, 23% is much higher than 4%
(b) 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 by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! 10/43 or 23.3% treated
2/46 or 4.3% control
at first glance, d is the best answer.
For the last question, b is the best answer. It is entirely possible that there is a real pain reduction, but the way to find out is to either to a Chi-Square test on the data, not compare percentages. With small sample sizes, this could be random error.
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