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

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
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Chapter11: Data Analysis And Probability
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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
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.
O yes, because more individuals in the treatment group were pain-free after 24 hours
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
O 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%
OIt is impossible to tell merely by comparing the sample proportions because the difference could be the
result of random error in our sample
Transcribed Image Text: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 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. O yes, because more individuals in the treatment group were pain-free after 24 hours 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 O 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% OIt is impossible to tell merely by comparing the sample proportions because the difference could be the result of random error in our sample
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