Step 1 :Given the 'before' and 'after' measurements, we first calculate the differences between these two sets of measurements. The differences are calculated as 'before - after'.
Step 2 :The differences are: \(2.6, 1.7, 1.2, 3.4, 4.2, -0.5, 2.3, -1.4\).
Step 3 :We then calculate the mean and standard deviation of these differences. The mean difference is approximately \(1.69\) and the standard deviation is approximately \(1.89\).
Step 4 :We use the formula for a confidence interval, which is given by \(\bar{x} \pm z \frac{s}{\sqrt{n}}\), where \(\bar{x}\) is the sample mean, \(z\) is the z-score corresponding to the desired confidence level (for a 95% confidence level, \(z = 1.96\)), \(s\) is the sample standard deviation, and \(n\) is the sample size.
Step 5 :Substituting the values into the formula, we get the 95% confidence interval for the mean of the 'before - after' differences as approximately \((0.38, 3.00)\).
Step 6 :Since this interval does not include zero and is entirely greater than zero, it indicates that there is a significant difference in pain before and after hypnotism. Therefore, hypnotism appears to be effective in reducing pain.
Step 7 :Final Answer: \(\boxed{\text{(D) Yes, because the confidence interval does not include zero and is entirely greater than zero.}}\)