A Visual Analog Scale (VAS) is a graphic rating tool used to gauge relative intensity of subjective measures such as feelings, attitudes, or opinions. A VAS consists of a horizontal line which represents a continuous scale, typically from a zero value at left to a maximum value at right. The line is marked at intervals, which may or may not be assigned numerical values or descriptors such as 'Never', 'Seldom', 'Sometimes', etc. Testers or subjects place an 'x' or other mark on the line representing the location of their perceived rating or self-rating. The VAS shown below has been used to self-report pain intensity.
For example, the pain intensity for the subject response below has a VAS value o 30.

In an acupuncture study 12 patients were randomly assigned to the acupuncture treatment and 8 to the placebo. The visual analog scale (VAS) was used to measure pain intensity before and after treatment for each patient in each treatment group. The tables on the next page give the results of this simulated study.
a. Is there sufficient evidence to conclude that acupuncture reduces pain intensity on average?

b. Is there sufficient evidence to conclude that the acupuncture treatment produces a higher mean reduction in VAS scores compared to the placebo?

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No Pain Worst Pain ACUPUNCTURE Pain Intensity Pain Intensity Difference Before (VAS) After Before-After (VAS) (VAS) 96 85 11 51 52 -1 41 41 21 24 -3 46 40 62 66 -4 61 58 58 43 15 85 79 6. 52 40 12 55 56 -1 62 59 3.