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 α=​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	2.6	1.8
2	2.1	1.6
3	1.7	1.3
4	3.3	2.6
5	3.4	2.7
6	3.9	2.3
7	3.6	2.8
8	2.9	2.5
9	2.9	1.6
10	3.5	2.9
11	3.6	1.3

(a) Identify the claim and state H0 and Ha.

The claim is​ "The therapy helps to reduce/helps to increase/does not change/changes the length of time patients suffer from​headaches."

Let μd be the hypothesized mean of the​ patients' daily headache hours before therapy minus their daily headache hours after it. State H0 and Ha.

Choose the correct answer below.

A. H0: μd ≤ 0

Ha​: μd > 0

B. H0​: μd ≠ d overbar

Ha​: μd = d overbar

C. H0​: μd ≥d overbar

Ha​: μd < d overbar

D. H0​: μd ≥ 0

Ha​: μd < 0

E. H0​: μd = d overbar

Ha​: μd ≠d overbar

F. H0​: μd ≤d overbar

Ha​: μd >d overbar

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

t0 = __________ (Use a comma to separate answers as needed. Type an integer or a decimal. Round to three decimal places as​ needed.)

Identify the rejection​ region(s). Choose the correct answer below.

A. t > 2.764

B. t < −2.764

t > 2.764

C. t < −3.169

t > 3.169

D. t < −3.169

​(c) Calculate d overbard.

d overbar = _________

​(Type an integer or a decimal. Round to three decimal places as​ needed.)

Calculate

s Subscript dsd.

s Subscript dsdequals=nothing ​(Type an integer or a decimal. Round to three decimal places as​ needed.)

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

t = ________ (Type an integer or a decimal. Round to three decimal places as​ needed.)

​(e) Decide whether to reject or fail to reject the null hypothesis. Choose the correct answer below.

a. Fail to reject the null hypothesis.

b. Reject the null hypothesis.

​(f) Interpret the decision in the context of the original claim. Choose the correct answer below.

A. Soft tissue therapy increases the length of time patients suffer from headaches.

B. The sample was not large enough to make a conclusion.

C. At the​ 1% significance​ level, there is not enough evidence that soft tissue therapy helps to reduce the length of time patients suffer from headaches.

D.At the​ 1% significance​ level, there is enough evidence that soft tissue therapy helps to reduce the length of time patients suffer from headaches.

Answer 1

a)

the claim is​ "The therapy helps to reduce  the length of time patients suffer from​headaches."

A. H0: μd ≤ 0

Ha​: μd > 0

b)

critical​ value :to =2.764

A. t > 2.764

c)

doverbar = 0.918

sd =0.588

d)

t =5.180

e)

b. Reject the null hypothesis.

f)

D.At the​ 1% significance​ level, there is enough evidence that soft tissue therapy helps to reduce the length of time patients suffer from headaches.