8.3. 3.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 1 2 3 4 5 6 7 8 9 10 11 Daily headache hours (before) 2.5 2.1 2.2 2.4 1.9 2.1 2.9 3.9 4.5 2.4 2.6 Daily headache hours (after) 2.0 1.2 1.7 1.3 1.4 1.3 1.5 2.5 2.0 1.7 1.4 (a) Identify the claim and state
8.3. 3.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 1 2 3 4 5 6 7 8 9 10 11 Daily headache hours (before) 2.5 2.1 2.2 2.4 1.9 2.1 2.9 3.9 4.5 2.4 2.6 Daily headache hours (after) 2.0 1.2 1.7 1.3 1.4 1.3 1.5 2.5 2.0 1.7 1.4 (a) Identify the claim and state
8.3. 3.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 1 2 3 4 5 6 7 8 9 10 11 Daily headache hours (before) 2.5 2.1 2.2 2.4 1.9 2.1 2.9 3.9 4.5 2.4 2.6 Daily headache hours (after) 2.0 1.2 1.7 1.3 1.4 1.3 1.5 2.5 2.0 1.7 1.4 (a) Identify the claim and state
8.3. 3.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
1
2
3
4
5
6
7
8
9
10
11
Daily headache hours (before)
2.5
2.1
2.2
2.4
1.9
2.1
2.9
3.9
4.5
2.4
2.6
Daily headache hours (after)
2.0
1.2
1.7
1.3
1.4
1.3
1.5
2.5
2.0
1.7
1.4
(a) Identify the claim and state
H0
and
Ha.
The claim is "The therapy
(1)
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
Ha:
μd≠d
C.
H0:
μd≤d
Ha:
μd>d
D.
H0:
μd≥0
Ha:
μd<0
E.
H0:
μd≥d
Ha:
μd<d
F.
H0:
μd≠d
Ha:
μd=d
(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<−3.169
or
t>3.169
B.
t<−3.169
C.
t<−2.764
or
t>2.764
D.
t>2.764
(c) Calculate
d.
d=
(Type an integer or a decimal. Round to three decimal places as needed.)
Calculate
sd.
sd=
(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.
Reject
the null hypothesis.
Fail to reject
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
is not
enough evidence that soft tissue therapy helps to reduce the length of time patients suffer from headaches.
B.
At the 1% significance level, there
is
enough evidence that soft tissue therapy helps to reduce the length of time patients suffer from headaches.
C.
The sample was not large enough to make a conclusion.
D.
Soft tissue therapy increases the length of time patients suffer from headaches.
(1)
does not change
helps to reduce
helps to increase
changes
Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.
