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 patients diagnosed with migraine headaches were randomly assigned to one of two groups: treatment or control.Patients in the treatment group received acupuncture that is specifically designed to treat migraines and 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. Test to see if migraine pain relief is dependent on receiving acupuncture. Test at the 8% level and round expected values to one decimal place. Pain Relief Yes (Observed) Yes (Expected Value) No (Observed) No (Expected Value) Row Total No Relief 29 29 58 Control 91 103 194 Column Total 120 132 252 H: Hypotheses Ho:Ho:Select an answer Treatment Migraine Control Yes and Select an answer Pain Relief Migraine Control No are Select an answer independent dependent Ha:Ha:Select an answer Treatment Migraine Control Yes and Select an answer Pain Relief Migraine Control No are Select an answer independent dependent Original Claim: Select an answer H₀ H₁ Enter the critical values, along with the significance level and degrees of freedom χ2χ2(αα,df) below the graph. (Graph is for illustration only. No need to shade.) X2Χ2( ,) = Test Statistic χ2χ2 = (Round to three decimal places.) P-value = (Round to four decimal places.) Decision: Select an answer reject H₀ fail to reject H₀ accept H₀ reject Hₐ fail to reject Hₐ . Conclusion: There Select an answer is is not significant evidence to conclude that Select an answer Treatment Migraine Control Yes and Select an answer Pain Relief Migraine Control No are Select an answer independent dependent

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 patients diagnosed with migraine headaches were randomly assigned to one of two groups: treatment or control.Patients in the treatment group received acupuncture that is specifically designed to treat migraines and 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. Test to see if migraine pain relief is dependent on receiving acupuncture. Test at the 8% level and round expected values to one decimal place. Pain Relief Yes (Observed) Yes (Expected Value) No (Observed) No (Expected Value) Row Total No Relief 29 29 58 Control 91 103 194 Column Total 120 132 252 H: Hypotheses Ho:Ho:Select an answer Treatment Migraine Control Yes and Select an answer Pain Relief Migraine Control No are Select an answer independent dependent Ha:Ha:Select an answer Treatment Migraine Control Yes and Select an answer Pain Relief Migraine Control No are Select an answer independent dependent Original Claim: Select an answer H₀ H₁ Enter the critical values, along with the significance level and degrees of freedom χ2χ2(αα,df) below the graph. (Graph is for illustration only. No need to shade.) X2Χ2( ,) = Test Statistic χ2χ2 = (Round to three decimal places.) P-value = (Round to four decimal places.) Decision: Select an answer reject H₀ fail to reject H₀ accept H₀ reject Hₐ fail to reject Hₐ . Conclusion: There Select an answer is is not significant evidence to conclude that Select an answer Treatment Migraine Control Yes and Select an answer Pain Relief Migraine Control No are Select an answer independent dependent

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Migraine and Acupuncture:

Pain Relief	Yes (Observed)	Yes (Expected Value)	No (Observed)	No (Expected Value)	Row Total
No Relief	29		29		58
Control	91		103		194
Column Total	120		132		252

H: Hypotheses

Ho:Ho:Select an answer Treatment Migraine Control Yes and Select an answer Pain Relief Migraine Control No are Select an answer independent dependent

Ha:Ha:Select an answer Treatment Migraine Control Yes and Select an answer Pain Relief Migraine Control No are Select an answer independent dependent

Original Claim: Select an answer H₀ H₁

Enter the critical values, along with the significance level and degrees of freedom χ2χ2_(αα,df) below the graph. (Graph is for illustration only. No need to shade.)

X2Χ2_( ,) =

Test Statistic χ2χ2 =  (Round to three decimal places.)

P-value =  (Round to four decimal places.)

Decision: Select an answer reject H₀ fail to reject H₀ accept H₀ reject Hₐ fail to reject Hₐ  .

Conclusion:

There Select an answer is is not significant evidence to conclude that Select an answer Treatment Migraine Control Yes and Select an answer Pain Relief Migraine Control No are Select an answer independent dependent .

Expert Solution

Step 1

Given data,

observed values,

Group	Yes	No	Total
Treatment	29	29	58
Control	91	103	194
Total	120	132	252

Null Hypothesis:

H₀: Migraine and pain relief are independent.

Alternative Hypothesis:

H₁: Migraine and pain relief are dependent.

Step 2

Expected value:

$E_{i} = \frac{R o w t o t a l \times C o l u m n t o t a l}{G r a n d t o t a l}$

Group	Yes	Expected values	No	Expected values	Total
Treatment	29	27.62	29	30.38	58
Control	91	92.38	103	101.62	194
Total	120		132		252

Degrees of freedom:

Df= (r-1)(c-1)

=(2-1)(2-1)

Critical value:

level of significance is 0.08.

critical value is 3.065.

Test statistics:

$χ^{2} = \sum_{}^{} \frac{{(O_{i} - E_{i})}^{2}}{E_{i}}$

From the above table,

The chi square test statistic is 0.171.

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