In the paper "An Analysis of Factors That Contribute to the Efficacy of Hypnotic Analgesia" (Journal of Abnormal Psychology, Vol. 96, No. 1, pp. 46-51), D. Price and J. Barber examined the effects of hypnosis on pain. They measured response to pain using a visual analogue scale (VAS), in centimeters, where higher VAS indicates greater pain. VAS sensory ratings were made before and after hypnosis on each of 16 subjects. A hypothesis test is to be performed to decide whether, on average, hypnosis reduces pain.
a. Identify the variable.
b. Identify the two populations.
c. Identify the pairs.
d. Identify the paired-difference variable.
e. Determine the null and alternative hypotheses.
f. Classify the hypothesis test as two tailed, left tailed, or right tailed.

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