Answered: A migraine is a particularly painful…

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter9: Sequences, Probability And Counting Theory

Section9.7: Probability

Problem 3SE: What is an experiment?

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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 98 females diagnosed with migraine headaches were randomly assigned to one of two groups: treatment or control. 45 patients in the treatment group received acupuncture that is specifically designed to treat migraines. 53 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.
(please round answers to within one hundredth of a percent)

	Pain Free: Yes	Pain Free: No	Total
Treatment	13	32	45
Control	4	49	53
Total	17	81	98

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

Expert Solution

Step 1: Introduce the given information

"Since you have posted a question with multiple subparts we will provide solutions only to the first three subparts as par our Q&A guidelines. Please repost the remaining subparts separately".

Here the given table is :-

	Pain Free:yes	Pain Free:No	Total
Treatment	13	32	45
Control	4	49	53
Total	17	81	98

Using formula,

$P r o b a b i l i t y space equals fraction numerator n u m b e r space o f space f a v o r a b l e space o u t c o m e s over denominator T o t a l space o u t c o m e s end fraction$