Question

The table below shows the number of hours per day 11 patients suffered from headaches before and after 7 weeks of soft tissue therapy. At alphaαequals= 0.01,is there enough evidence to conclude that soft tissue therapy helps to reduce the length of time patients suffer from headaches? Assume the samples are random and dependent, and the population is normally distributed. Complete parts (a) through (f).

Patient	Daily headache hours (before)	Daily headache hours (after)
1	4.1	2.2
2	2.2	1.6
3	1.8	1.2
4	2.3	1.4
5	3.3	2.8
6	2.5	1.6
7	3.7	2.1
8	2.2	1.4
9	2.3	1.6
10	3.6	2.8
11	3.3	1.5

A. State Ho and Ha

B.Find the critical value(s) and identify the rejection region(s).

Identify the rejection region(s)

C. (c) Calculated overbard.

Calculate s Subscript dsd.

D. (d) Use the t-test to find the standardized test statistic t.

(e) Decide whether to reject or fail to reject the null hypothesis.

(f) Interpret the decision in the context of the original claim. .

Answer 1

The following table is obtained:

	Sample 1	Sample 2	Difference = Sample 1 - Sample 2
	4.1	2.2	1.9
	2.2	1.6	0.6
	1.8	1.2	0.6
	2.3	1.4	0.9
	3.3	2.8	0.5
	2.5	1.6	0.9
	3.7	2.1	1.6
	2.2	1.4	0.8
	2.3	1.6	0.7
	3.6	2.8	0.8
	3.3	1.5	1.8
Average	2.845	1.836	1.009
St. Dev.	0.77	0.559	0.507
n	11	11	11

From the sample data, it is found that the corresponding sample means are: