Question

A study was conducted to investigate the effectiveness of hypnotism in reducing pain. Results for randomly selected subjects are given in the accompanying table. The mesurements are centimeters on pain scale.

Use a 0.05 significance level to test the claim that the sensory measurements are lower after hypnotism

Subjects 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 either the critical value or the P-value method

a) State the claim and hypothesis

b) Find the critical value(s) and describe the critical (rejection) region. You can choose to use the P-value method in this case state the P-value after the test value.

c) compute the test value (statistic)

d) MMake a decision

e) Summarize the results (conclusion)

Answer 1

a)

Null hypothsis

claim that the sensory measurements remain same after hypnotism

Alternative hypothesis

claim that the sensory measurements are lower after hypnotism

b)

c)

test statistic=

where Sz standard deviation of z

n=8,

S_z= 2.91143

Hence t=3.04

pvalue = 0.009

d)

As p value is less than 0.05 we would reject the null hypothesis.

Again as t=3.04 is greater than the critical value t_7;0.05=1.895 we woul reject the null hypothesis.

e)

So we can conclude that at 0.05 level of significance the sensory measurements are lower after hypnotism.

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