Is acupuncture effective on back pain? Patients with chronic low back pain were randomly assigned to one of four groups. Some patients received standardized acupuncture, while others received acupuncture that was individualized. A third group was given simulated acupuncture in which a toothpick was used but the skin was not penetrated. A fourth group received medical care that did not include acupuncture. The researchers recorded whether or not each patient improved by at least 3 points on the Roland-Morris Disability Questionnaire scale. The following table shows the data. Is there evidence of an association between treatment group and improvement?
Here is computer output for a chi-square test to compare the four groups.
X-squared = 8.93, df = 3, p-value = 0.0302
(a) State the null and alternative hypotheses in context.
(b) Compute the observed "Yes" percentages for each of the four groups.
(c) If α = 0.05, what is your conclusion regarding H0?

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Individualized Standardized Simulated Usual care Total 350 233 92 49 141 72 71 143 Improved? Yes No Total 96 51 147 90 62 152