Matched or Paired Samples · Example 1

A study was conducted to investigate the effectiveness of hypnotism in reducing pain. Results for randomly selected subjects are shown in the table. A lower score indicates less pain. The "before" value is matched to an "after" value and the differences are calculated. The differences have a normal distribution. Are the sensory measurements, on average, lower after hypnotism? Test at a 5% significance level.

$$\begin{array}{ccccccccc}\text{Subject:}& \text{A}& \text{B}& \text{C}& \text{D}& \text{E}& \text{F}& \text{G}& \text{H}\\ \text{Before}& \text{6.6}& \text{6.5}& \text{9.0}& \text{10.3}& \text{11.3}& \text{8.1}& \text{6.3}& \text{11.6}\\ \text{After}& \text{6.8}& \text{2.4}& \text{7.4}& \text{8.5}& \text{8.1}& \text{6.1}& \text{3.4}& \text{2.0}\end{array}$$

Its source prints no answer for this problem, so there's nothing to check against.

OpenStax, Introductory Statistics 2e · §10.4 Matched or Paired Samples · Example 1