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A researcher would like to determine if relaxation training will affect the number of headaches for chronic headache sufferers. For a week prior to training, each participant records the number of headaches suffered. Participants then receive relaxation training, and for the week following training the number of headaches is again measured. The change in number of headaches before and after training is as follows (minus signs indicate a reduction).
Difference scores: -5 -1 -4 -3 -6 -8 0 +1 -1

(a) Compute the mean and SS for the sample of difference scores.
MD = ______
SS = ________

(b) Do the results indicate a significant difference? Use a two-tailed test with &#945; = .05.

A. Yes, the relaxation training has a significant effect.
B. No, the relaxation training hasn't any significant effect.

(c) Compute r2, the percentage of variance accounted for, to measure the size of the effect. (Round the answer to two decimal places.)
r2 = _______

#### Solution Preview

a)
Number of observations = 9
The mean = [-5 + -1 + -4 + -3 + -6 + -8 + 0 + 1 - 1]/9 = -27/9 = -3

SS = sum of the squares of the difference between observations and mean.

= (-5 - (-3))^2 + (-1 - (-3))^2 +............(-1 - (-3))^2 , where ^ means raised to the power of

Thus, SS in this case = 72

b)
We perform a 1 sample t test to see if the mean of the difference is significantly different from 0.

Independent one-sample t-test
In testing the null hypothesis that the population mean is equal to a specified value &#956;0, one uses the statistic
t = (x - &#956;0)/(s/n^0.5)
where x is sample mean and s is the sample standard deviation of the sample and n is the sample size.
The degrees of freedom used in this test is n &#8722; 1.

p value can be found from a student's t table.

DF 0.200 0.100 0.0500 0.0200 0.0100 0.00500 0.00200 0.001 -> p values
1 3.078 6.314 12.706 31.820 63.657 127.321 318.309 636.619
2 1.886 2.920 4.303 6.965 9.925 14.089 22.327 31.599
3 1.638 2.353 3.182 4.541 5.841 7.453 10.215 12.924
4 1.533 2.132 2.776 3.747 4.604 5.598 7.173 8.610
5 1.476 2.015 2.571 3.365 4.032 4.773 5.893 6.869
6 ...

#### Solution Summary

How to test a hypothesis about whether relaxation training affects the number of chronic headaches?

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