Acupuncture. Research reported in 2008 brings to lightthe effectiveness of treating chronic lower back pain withdifferent methods. One-third of nearly 1200 volunteers were administered conventional treatment (drugs, physi-cal therapy, and exercise). The remaining patients got 30-minute acupuncture sessions. Half of these patientswere punctured at sites suspected of being useful andhalf received needles at other spots on their bodies.Comparable shares of each acupuncture group, roughly45%, reported decreased back pain for at least six monthsafter their sessions ended. This was almost twice as highas those receiving the conventional therapy, leading theresearchers to conclude that results were statisticallysignificant.a) Why did the researchers feel it was necessary to havesome of the patients undergo a “fake” acupuncture?b) Because patients had to consent to participate in thisexperiment, the subjects were essentially self-selected—a kind of voluntary response group. Explain why thatdoes not invalidate the findings of the experiment.c) What does “statistically significant” mean in thecontext of this experiment?

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.