In a study reported in the September 24, 2007, issue of the Archives of Internal Medicine, German researchers described a study conducted on 1162 German adults suffering from chronic low-back pain. These subjects were randomly assigned to one of three groups: real acupuncture, sham acupuncture, and conventional therapy. Researchers found that

47 \%

of subjects in the real acupuncture group improved, compared to

44 \%

in the sham acupuncture group and

27 \%

in the conventional therapy group.
a. Identify the observational units in this study.
b. Identify the explanatory variable. Also classify it as categorical or quantitative.
If it is categorical, indicate whether it is binary.
c. Identify the response variable.
d. Is this an observational study or an experiment? Explain briefly.
e. Did this study make use of random assignment or random sampling, or both, or neither? Explain briefly.
f. Construct an appropriate graph to display the results.
g. Comment on what the graph reveals.
h. If the researchers find that the difference in improvement percentages between the real acupuncture group and the conventional therapy group is significant, would it be appropriate to conclude that real acupuncture causes a higher improvement rate than conventional therapy? Explain.

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An Organization Called the Knot Inc $\$ 26,984$ And That $43 \%$

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