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

alphaequals=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	1	2	3	4	5	6	7	8	9	10	11
Daily headache hours left parenthesis before right parenthesisDailyheadachehours(before)	3.2	2.2	3.8	3.4	4.2	2.6	3.2	1.6	2.7	4.3	3.3
Daily headache hours (after)	2.6	1.7	1.5	1.5	1.6	1.5	1.3	1.1	1.3	3.4	2.0

Question content area bottom

Part 1

(a) Identify the claim and state

Upper H 0H0

and

Upper H Subscript aHa.

The claim is "The therapy

does not change

changes

helps to reduce

helps to increase

the length of time patients suffer from headaches."

Part 2

Let

mu Subscript dd

be the hypothesized mean of the patients' daily headache hours before therapy minus their daily headache hours after it. State

Upper H 0H0

and

Upper H Subscript aHa.

Choose the correct answer below.

A.

Upper H 0H0:

mu Subscript ddless than or equals0

Upper H Subscript aHa:

mu Subscript ddgreater than>0

B.

Upper H 0H0:

mu Subscript ddgreater than or equals0

Upper H Subscript aHa:

mu Subscript ddless than<0

C.

Upper H 0H0:

mu Subscript ddequals=d overbard

Upper H Subscript aHa:

mu Subscript ddnot equalsd overbard

D.

Upper H 0H0:

mu Subscript ddless than or equalsd overbard

Upper H Subscript aHa:

mu Subscript ddgreater than>d overbard

E.

Upper H 0H0:

mu Subscript ddnot equalsd overbard

Upper H Subscript aHa:

mu Subscript ddequals=d overbard

F.

Upper H 0H0:

mu Subscript ddgreater than or equalsd overbard

Upper H Subscript aHa:

mu Subscript ddless than

Part 3

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

t 0t0equals=enter your response here

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

Part 4

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

A.

tless than

or

tgreater than>3.169

B.

tless than

C.

tgreater than>2.764

D.

tless than

or

tgreater than>2.764

Part 5

(c) Calculate

d overbard.

d overbardequals=enter your response here

type integer or a decimal. Round to three decimal places as needed.)

Part 6

Calculate

s Subscript dsd.

s Subscript dsdequals=enter your response here

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

Part 7

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

tequals=enter your response here

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

Part 8

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

Fail to rejectFailtoreject

the null hypothesis.

RejectReject

the null hypothesis.

Part 9

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

Part 10

A.

At the 1% significance level, there

is notisnot

enough evidence that soft tissue therapy helps to reduce the length of time patients suffer from headaches.

B.

At the 1% significance level, there

isis

enough evidence that soft tissue therapy helps to reduce the length of time patients suffer from headaches.

C.

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

D.

The sample was not large enough to make a conclusion.

The claim is "The therapythe length of time patients suffer from headaches.Choose the correct answer below.t 0(Use a comma to separate answers as needed. Type an integer or a decimal. Round to three decimal places as needed.)Choose the correct answer below.d overbar(Type an integer or a decimal. Round to three decimal places as needed.)s Subscript d(Type an integer or a decimal. Round to three decimal places as needed.)t(Type an integer or a decimal. Round to three decimal places as needed.)Choose the correct answer below.Choose the correct answer below.