Question

A research team is interested in the effectiveness of hypnosis in reducing pain. The responses from 8 randomly selected patients before and after hypnosis are recorded in the table below (higher values indicate more pain). Construct a 90% confidence interval for the true mean difference in pain after hypnosis. Perceived pain levels 'Pre' and 'Post' hypnosis for 8 subjects

Pre 6.7 7.1 10.2 10.2 9.1 9.6 11.1 7.2

Post 9.5 11.5 11.3 8.4 10.9 10.2 8.4 10.6

Difference

a) Fill in the missing table cells for the pain level differences. Compute the differences as 'Pre - Post'.

b) If the hypnosis treatment is effective in reducing pain, we expect the differences (pre - post) to be .

Note: For (c), (d), and (e) use 3 decimals in your answers. You should use JMP to calculate these values.

c) The point estimate for the true average effect that hypnosis has on pain perception (i.e. xdifference) is:

d) The point estimate for the true standard deviation of the effect that hypnosis has on pain perception (i.e. sdifference)is:

e) The standard error for the mean difference in pain scores is:

f) For this problem, the sample size is small enough that approximating the critical value as being t = 2 will induce substantial error. It turns out that, for a sample size of n = 8, the 95% t-critical value is about t = 2.4. Using this, this 95% confidence interval for the true mean difference in pain level after hypnosis is: IMPORTANT: don't enter the 95% CI JMP gives you. It will be wrong, because t-critical = 2.4 has been rounded to the nearest decimal, while JMP uses a more precise value. You need to calculate this yourself using the CI formula. 95% CI for μdifference: to (round your answer to 2 decimals)

g) Based on your confidence interval in part (f), does the data seem to suggest strong evidence that this form of hypnosis has an effect on pain? Why or why not? (You have two attempts.) No, because 0 is in the confidence interval for the true mean difference.

No, because 0 is not in the confidence interval for the true mean difference.

Yes, because 0 is in the confidence interval for the true mean difference.

Yes, because 0 is not in the confidence interval for the true mean difference.

No, because the sample mean difference is in the confidence interval for the true mean difference.

No, because the sample mean difference is not in the confidence interval for the true mean difference.

Yes, because the sample mean difference is in the confidence interval for the true mean difference.

Yes, because the sample mean difference is not in the confidence interval for the true mean difference.

Answer 1

a)

Pre	Post	Difference
6.7	9.5	-2.8
7.1	11.5	-4.4
10.2	11.3	-1.1
10.2	8.4	1.8
9.1	10.9	-1.8
9.6	10.2	-0.6
11.1	8.4	2.7
7.2	10.6	-3.4

b) If the hypnosis treatment is effective in reducing pain, we expect the differences (pre - post) to be more than 0.

c)

∑d = -9.6

∑d² = 54.1

n = 8

point estimate, x̅d = Ʃd/n = -9.6/8 = -1.2

d) Standard deviation, sd = √[(Ʃd² - (Ʃd)²/n)/(n-1)] = √[(54.1-(-9.6)²/8)/(8-1)] = 2.4663

e) Standard error = sd/√n = 0.8720

f)

95% Confidence interval :

At α = 0.05 and df = n-1 = 7, two tailed critical value, t-crit = T.INV.2T(0.05, 7) = 2.400

Lower Bound = x̅d - t-crit*sd/√n = -1.2 - 2.4 * 2.4663/√8 = -3.29

Upper Bound = x̅d + t-crit*sd/√n = -1.2 + 2.4 * 2.4663/√8 = 0.89

g)

No, because 0 is in the confidence interval for the true mean difference.