In a study of the use of hypnosis to relieve pain sensory ra

In a study of the use of hypnosis to relieve pain, sensory ratings were measured for a random sample of 8 subjects, with the results given below. These subjects were hypnotized and then gave ratings of the level of pain experienced.

8.8

6.6

8.4

6.5

8.4

7.0

9.2

10.0

Is there sufficient evidence to conclude the population mean sensory score for people using hypnosis is less than 8.5? Explain your conclusion and supply statistical evidence.

the null and alternative hypothesis;

the p-value;

the decision to reject the null hypothesis or fail to reject; and

a final conclusion sentence about the question in the problem.

Solution

the null and alternative hypothesis;

Let mu be the population mean

Null hypothesis: mu=8.5

Alternative hypothesis: mu<8.5

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the p-value;

sample mean=8.1125

sample standard deviation =1.282227

The test statistic is

t=(xbar-mu)/(s/vn)

=(8.1125-8.5)/(1.282227/sqrt(8))

=-0.85

It is a left-tailed test.

The degree of freedom =n-1=8-1=7

So the p-value = P(t with df=7 <-0.85) =0.2117 (from student t table)

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the decision to reject the null hypothesis or fail to reject; and

Assume that the significant level a=0.05

Since the p-value is larger than 0.05, we do not reject the null hypothesis.

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a final conclusion sentence about the question in the problem.

So we can not conclude that the population mean sensory score for people using hypnosis is less than 8.5