Question

5. Effectiveness of Hypnotism in Reducing Back Pain

A study was conducted to investigate the effectiveness of hypnotism in reducing back pain. The values are before and after hypnosis and are measurements given on a pain scale. [Journal of Abnormal Psychology, Vol 96, No. 1, Price & Barber]      [3 decimal places]

Subject               A            B             C             D               E             F             G            H           

Before                  6.6         6.5         9.0         10.3               11.3       8.1         6.3         11.6

After                     6.8         2.4         7.4         8.5               8.1         6.1         3.4         2.0

Use α= 0.05 to test the claim that the mean sensory measurements are lower after hypnotism.

a) Hypothesis Statements           H_o: ___________                    H_a: _______________

b) Which of these statements is the claim? __________

c) Sketch the curve and identify the rejection zone(s), critical value(s) and std test statistic.

d) Critical Value(s) = ________     [label on the drawing]

e) Standardized Test Statistic = _________               [label on the drawing]

h) State your conclusion in terms of the original claim:

_____________________________________________________________________________________

i) Does hypnosis appear to be effective for reducing pain? _________

Answer 1

Part a

H₀: The mean sensory measurements are same for before and after hypnotism.

H_a: The mean sensory measurements are lower after hypnotism.

H₀: µ_d = 0 versus H_a: µ_d < 0

We assume d = after minus before

b) Which of these statements is the claim?

Claim: H_a: The mean sensory measurements are lower after hypnotism.

c) Sketch the curve and identify the rejection zone(s), critical value(s) and std test statistic.

From given data, we have

Dbar = -3.1250

S_d = 2.9114

n = 8

df = n – 1 = 7

α = 0.05

d) Critical Value(s) =

Critical value = -1.8946

(by using t-table)

e) Standardized Test Statistic =

Test statistic for paired t test is given as below:

t = (Dbar - µ_d)/[S_d/sqrt(n)]

t = (-3.1250 – 0)/[ 2.9114/sqrt(8)]

t = -3.0359

P-value = 0.0095

(by using t-table)

h) State your conclusion in terms of the original claim:

P-value < α = 0.05

So, we reject the null hypothesis

There is sufficient evidence to conclude that the mean sensory measurements are lower after hypnotism.

i) Does hypnosis appear to be effective for reducing pain?

Yes, there is sufficient evidence to conclude that the hypnosis appear to be effective for reducing pain.