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 there were fewer people in the treatment group no, because more than half of the individuals in the treatment group still experience pain 24 hours later 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
Question
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 there were fewer people in the treatment group no, because more than half of the individuals in the treatment group still experience pain 24 hours later 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
Solution
a) The percentage of patients in the treatment group who were pain free 24 hours after receiving acupuncture can be calculated by dividing the number of pain free patients in the treatment group by the total number of patients in the treatment group and then multiplying by 100.
So, (10/43) * 100 = 23.26%.
b) The percentage of patients in the control group who were pain free 24 hours after receiving acupuncture can be calculated by dividing the number of pain free patients in the control group by the total number of patients in the control group and then multiplying by 100.
So, (2/46) * 100 = 4.35%.
c) At first glance, acupuncture does not appear to be an effective treatment for migraines because more than half of the individuals in the treatment group still experience pain 24 hours later.
d) It is impossible to tell merely by comparing the sample proportions because the difference could be the result of random error in our sample. While the percentage of pain-free individuals in the treatment group is higher than in the control group, this does not necessarily mean that acupuncture is an effective treatment for migraines. Further statistical analysis would be needed to determine if this difference is statistically significant.
Similar Questions
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