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	11.3	8.1	8.4	11.1	13.4	15.1	10.6	10.1
Post	9.9	9.1	3.1	8.5	7.0	9.9	10.9	7.7
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  ---Select---  positive negative zero even odd prime .

Now enter the column of the differences in Excel. In ToolPak, use the descriptive statistics option with the Confidence Level for the mean as 95% to get the output you'll need for the following questions. Note: For (c), (d), and (e) use 3 decimals in your answers.

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

d) The point estimate for the true standard deviation of the effect that hypnosis has on pain perception (i.e. s_d)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 slightly larger than 2. Excel uses the true critical value when finding the margin of error, which it calls the "Confidence Level". Using this margin of error, the 95% confidence interval for the true mean difference in pain level after hypnosis is:



95% CI for μ_d:(  ,  )
(round your answer to 2 decimals and put the smaller number first)

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	11.3	8.1	8.4	11.1	13.4	15.1	10.6	10.1
Post	9.9	9.1	3.1	8.5	7	9.9	10.9	7.7
Difference	1.4	-1	5.3	2.6	6.4	5.2	-0.3	2.4

b)

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

c)

The point estimate for the true average effect that hypnosis has on pain perception (i.e. x_d) is 2.750

d)

The point estimate for the true standard deviation of the effect that hypnosis has on pain perception (i.e. s_d)is: 2.703

e)

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

f)

g)

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