Answered: 8.3. 3.The table below shows the number…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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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

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

and

Ha.

Choose the correct answer below.

H0:

μd≤0

Ha:

μd>0

H0:

μd=d

Ha:

μd≠d

H0:

μd≤d

Ha:

μd>d

H0:

μd≥0

Ha:

μd<0

H0:

μd≥d

Ha:

μd<d

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.

t<−3.169

t>3.169

t<−3.169

t<−2.764

t>2.764

(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.

(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.

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.

At the 1% significance level, there

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

The sample was not large enough to make a conclusion.

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.

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