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 a=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 rando 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) 2.3 4.1 3.2 3.5 2.4 3.7 2.6 3.4 3.3 2.6 1.8 Daily headache hours (after) 1.8 2.7 1.8 1.6 1.9 1.9 1.2 2.5 2.2 2.0 1.1 C (a) Identify the claim and state Ho and H₂ The claim is "The therapy the length of time patients suffer from headaches." Let u be the hypothesized mean of the patients' daily headache hours before therapy minus their daily headache hours after it. State Ho and H₂. Choose the correct answer below. OA. Ho: Hg = OB. Hg: Hg Sd H₂: Had H₂: Hgd H₂:0 06, Hoi Hy 50 OF Hoi Hy 20 H₂: Hg <0 OD. Ho: Pg #d H₁: Pg=d OE H₂: Mg 2 Најњед (b) Find the critical value(s) and identify the rejection region(s). (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. OA. <-3.169 or t>3.169 OB. <-2.764 or 1>2.764 OC. t-3.169 OD. 1>2.764 (c) Calculate d. (Type an integer or a decimal. Round to three decimal places as needed.) Calculate - (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 (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. O Reject the null hypothesis. O Fail to reject the null hypothesis. (1) Interpret the decision in the context of the original claim. Choose the correct answer below. OA. 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. OB. The sample was not large enough to make a conclusion. OC. Soft tissue therapy increases the length of time patients suffer from headaches. OD. At the 1% significance level, there is enough evidence that soft tissue therapy helps to reduce the length of time patients suffer from headaches.
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 a=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 rando 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) 2.3 4.1 3.2 3.5 2.4 3.7 2.6 3.4 3.3 2.6 1.8 Daily headache hours (after) 1.8 2.7 1.8 1.6 1.9 1.9 1.2 2.5 2.2 2.0 1.1 C (a) Identify the claim and state Ho and H₂ The claim is "The therapy the length of time patients suffer from headaches." Let u be the hypothesized mean of the patients' daily headache hours before therapy minus their daily headache hours after it. State Ho and H₂. Choose the correct answer below. OA. Ho: Hg = OB. Hg: Hg Sd H₂: Had H₂: Hgd H₂:0 06, Hoi Hy 50 OF Hoi Hy 20 H₂: Hg <0 OD. Ho: Pg #d H₁: Pg=d OE H₂: Mg 2 Најњед (b) Find the critical value(s) and identify the rejection region(s). (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. OA. <-3.169 or t>3.169 OB. <-2.764 or 1>2.764 OC. t-3.169 OD. 1>2.764 (c) Calculate d. (Type an integer or a decimal. Round to three decimal places as needed.) Calculate - (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 (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. O Reject the null hypothesis. O Fail to reject the null hypothesis. (1) Interpret the decision in the context of the original claim. Choose the correct answer below. OA. 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. OB. The sample was not large enough to make a conclusion. OC. Soft tissue therapy increases the length of time patients suffer from headaches. OD. At the 1% significance level, there is enough evidence that soft tissue therapy helps to reduce the length of time patients suffer from headaches.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section: Chapter Questions
Problem 22SGR
Related questions
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 x = 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
8 9 10 11 Q
1
Daily headache hours (before) 2.3
3.4 3.3 2.6 1.8
Daily headache hours (after) 1.8 2.7 1.8 1.6 1.9 1.9 1.2 2.5 2.2 2.0 1.1
2 3 4 5 6 7
4.1 3.2 3.5 2.4 3.7 2.6
C
(a) Identify the claim and state Ho and Ha
The claim is "The therapy
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 Ho and H₂. Choose the correct answer below.
OA. Ho: Hd=d
O C. Ho: Hd ≤0
OB. Ho. Họ sở
Ha: Hd >d
Ha: Hdd
Ha: Hd>0
OD. Ho: Hd #d
Ha:Hd=d
O E. Ho: Hd zd
Ha: Hd <d
OF. Ho: Hd 20
Ha: Hd <0
(b) Find the critical value(s) and identify the rejection region(s).
to =
(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.
O A. t - 3.169 or t> 3.169
O B. t< -2.764 or t>2.764
OC. t - 3.169
O 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.
O Reject the null hypothesis.
O
Fail to reject the null hypothesis.
(f) Interpret the decision in the context of the original claim. Choose the correct answer below.
O 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.
O B. The sample was not large enough to make a conclusion.
O C. Soft tissue therapy increases the length of time patients suffer from headaches.
O D. At the 1% significance level, there enough evidence that soft tissue therapy helps to reduce the length of time patients suffer from headaches.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffcda2731-ebd9-4775-b731-24a6f5547ea5%2Ff3b8ea1a-864e-4ffb-97f5-e2aa4f81e085%2F2kunez_processed.png&w=3840&q=75)
Transcribed Image Text: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 x = 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
8 9 10 11 Q
1
Daily headache hours (before) 2.3
3.4 3.3 2.6 1.8
Daily headache hours (after) 1.8 2.7 1.8 1.6 1.9 1.9 1.2 2.5 2.2 2.0 1.1
2 3 4 5 6 7
4.1 3.2 3.5 2.4 3.7 2.6
C
(a) Identify the claim and state Ho and Ha
The claim is "The therapy
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 Ho and H₂. Choose the correct answer below.
OA. Ho: Hd=d
O C. Ho: Hd ≤0
OB. Ho. Họ sở
Ha: Hd >d
Ha: Hdd
Ha: Hd>0
OD. Ho: Hd #d
Ha:Hd=d
O E. Ho: Hd zd
Ha: Hd <d
OF. Ho: Hd 20
Ha: Hd <0
(b) Find the critical value(s) and identify the rejection region(s).
to =
(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.
O A. t - 3.169 or t> 3.169
O B. t< -2.764 or t>2.764
OC. t - 3.169
O 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.
O Reject the null hypothesis.
O
Fail to reject the null hypothesis.
(f) Interpret the decision in the context of the original claim. Choose the correct answer below.
O 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.
O B. The sample was not large enough to make a conclusion.
O C. Soft tissue therapy increases the length of time patients suffer from headaches.
O D. At the 1% significance level, there enough evidence that soft tissue therapy helps to reduce the length of time patients suffer from headaches.
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