Question

a) what percent of patients in the treatment group were pain free 24 hours after receiving acupuncture? 29.82 % b) what percent of patients in the control group were pain free after 24 hours? 6.06 % c) at first glance, does acupuncture appear to be an effective treatment for migraines? explain your reasoning. yes, because a higher percentage of individuals in the treatment group were pain - free after 24 hours. 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. 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? it is impossible to tell merely by comparing the sample proportions because the difference could be the result of random error in our sample. yes, the percentage of patients in the treatment group who were pain free 24 hours after treatment was much greater than the corresponding percentage of patients in the control group.

Explanation:

Step1: Calculate percentage for treatment group

The formula for percentage is $\frac{\text{Number of pain - free in treatment}}{\text{Total in treatment}}\times100$. So, $\frac{17}{57}\times 100\approx 29.82\%$.

Step2: Calculate percentage for control group

Using the percentage formula $\frac{\text{Number of pain - free in control}}{\text{Total in control}}\times100$, we have $\frac{2}{33}\times 100\approx 6.06\%$.

Step3: Answer part c

The percentage of pain - free in the treatment group ($29.82\%$) is higher than in the control group ($6.06\%$). So, acupuncture appears effective because a higher percentage of individuals in the treatment group were pain - free after 24 hours.

Step4: Answer part d

Just comparing sample proportions, the difference could be due to random error in the sample. It is impossible to tell merely by comparing the sample proportions.

Answer:

a) $29.82\%$
b) $6.06\%$
c) Yes, because a higher percentage of individuals in the treatment group were pain - free after 24 hours.
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.