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   3.1   2.4
2   1.8   2.2
3   3.4   1.2
4   3.7   3.2
5   2.3   1.5
6   3.4   1.7
7   1.6   1.4
8   2.6   2.4
9   4.2   3.4
10   2.7   1.3
11   3.3   4.0

(a) Identify the claim and state

Upper H 0H0

and

Upper H Subscript aHa.

The claim is​ "The therapy

helps to reduce

the length of time patients suffer from​ headaches."Let

mu Subscript dμd

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 dμdless than or equals≤d overbard

Upper H Subscript aHa​:

mu Subscript dμdgreater than>d overbard

B.

Upper H 0H0​:

mu Subscript dμdgreater than or equals≥d overbard

Upper H Subscript aHa​:

mu Subscript dμdless than<d overbard

C.

Upper H 0H0​:

mu Subscript dμdgreater than or equals≥0

Upper H Subscript aHa​:

mu Subscript dμdless than<0

D.

Upper H 0H0​:

mu Subscript dμdequals=d overbard

Upper H Subscript aHa​:

mu Subscript dμdnot equals≠d overbard

E.

Upper H 0H0​:

mu Subscript dμdnot equals≠d overbard

Upper H Subscript aHa​:

mu Subscript dμdequals=d overbard

F.

Upper H 0H0​:

mu Subscript dμdless than or equals≤0

Upper H Subscript aHa​:

mu Subscript dμdgreater than>0

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

t 0t0equals=nothing

​(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.

tless than<minus−3.169

or

tgreater than>3.169

B.

tless than<minus−2.764

or

tgreater than>2.764

C.

tgreater than>2.764

D.

tless than<minus−3.169

​(c) Calculate

d overbard.

d overbardequals=nothing

​(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.

tequals=nothing

​(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.

Fail to rejectFail to reject

the null hypothesis.

RejectReject

the null hypothesis.

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

A.At the​ 1% significance​ level, there

isis

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

B.

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

C.

The sample was not large enough to make a conclusion.

D.At the​ 1% significance​ level, there

is notis not

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

Click to select your answer(s).

Answer 1

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