A research team is interested in the effectiveness of hypnosis in reducing pain.

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.

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 positive .

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. xd) is:

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

e) The 90% critical value is:

f) The 90% confidence interval for the true mean difference in pain level after hypnosis is:
< d <
(round your answer to 2 decimals)

g) Based on your confidence interval in part (f), does hypnosis seem to have a significant effect on pain levels? Why or why not?

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.

Perceived pain levels 'Pre' and 'Post' hypnosis for 8 subjects Pre 7.5 6.8 6.2 7.8 6.4 8.7 10.5 7.5 Post 5.8 8.3 9.3 6.7 7.5 7.4 9.0 8.6 Difference

Explanation / Answer

Confidence Interval
CI = d ± t a/2 * (Sd/ Sqrt(n))
Where,
d = di/n
Sd = Sqrt( di^2 – ( di )^2 / n ] / ( n-1 ) )
a = 1 - (Confidence Level/100)
ta/2 = t-table value
CI = Confidence Interval
d = ( di/n ) =-1.2/8=-0.15
Pooled Sd( Sd )= Sqrt [ 22.32- (-1.2^2/8 ] / 7 = 1.778
Confidence Interval = [ -0.15 ± t a/2 ( 1.027/ Sqrt ( 8) ) ]
= [ -0.15 - 1.895 * (0.629) , -0.15 + 1.895 * (0.629) ]
= [ -1.342 , 1.042 ]

[ANSWERS]
a. 1.7
-1.5
-3.1
1.1
-1.1
1.3
1.5
-1.1

c.
point estimate = -0.15
e.
critical value is 1.895
f.
[ -1.342 , 1.042 ]

X Y X-Y (X-Y)^2 7.5 5.8 1.7 2.89 6.8 8.3 -1.5 2.25 6.2 9.3 -3.1 9.61 7.8 6.7 1.1 1.21 6.4 7.5 -1.1 1.21 8.7 7.4 1.3 1.69 10.5 9 1.5 2.25 7.5 8.6 -1.1 1.21 -1.2 22.32

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