A.) What is the sample mean difference in inflammation between no massage and massage?sample mean difference=?(exact number)B.)We want to test to see if the population mean difference is greater than zero, meaning muscle with no treatment has more inflammation than muscle that has been massaged.State the null and alternative hypothesisHo= Ha=C.)Use StatKey or other technology to find the P-value from a randomization distribution.P-value=?Round your answer to three decimal places. We want to test to see if the population mean difference \( \mu_D \) is greater than zero, meaning muscle with no treatment has more inflammation than muscle that has been massaged.State the null and alternative hypotheses.Use \( \mu \) instead of \( \mu_D \) to answer this question.Equation Editor:\[ = \quad \neq \quad < \quad > \quad \mu \quad \mu_1 \quad \mu_2 \quad p \quad p_1 \quad p_2 \quad 0 \quad \rho \quad \bar{x} \quad \bar{x}_1 \quad \bar{x}_2 \quad \hat{p} \quad \hat{p}_1 \quad \hat{p}_2 \quad r \]Formulate:\[ H_0: \quad \_ \quad \_ \quad \_ \quad \text{vs} \quad H_a: \quad \_ \quad \_ \quad \_ \] **Does Massage Help Heal Muscles Strained by Exercise?**After exercise, massage is often used to relieve pain, and a recent study¹ shows that it also may relieve inflammation and help muscles heal. In the study, eleven male participants who had just strenuously exercised had 10 minutes of massage on one quadricep and no treatment on the other, with treatment randomly assigned. After 2.5 hours, muscle biopsies were taken and production of the inflammatory cytokine interleukin-6 was measured relative to the resting level. The differences (control minus massage) are given in Table 1 below.```+-----+-----+-----+-----+-----+------+-----+-----+| 0.6 | 4.7 | 3.8 | 0.4 | 1.5 | -1.2 | 2.8 | -0.4 | 1.4 | 3.5 | -2.8 |+-----+-----+-----+-----+-----+------+-----+-----+```*Table 1: Inflammation in muscle: control minus massage*¹ Data approximated from summary statistics in Crane, et al., "Massage Therapy Attenuates Inflammatory Signaling After Exercise-Induced Muscle Damage," *Science Translational Medicine*, 1 February 2012.Click [here](#) to access StatKey.

A) Consider that µ is the population mean difference of control and massage group.

Answered: A.) What is the sample mean difference…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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A.) What is the sample mean difference in inflammation between no massage and massage?

sample mean difference=?(exact number)

B.)We want to test to see if the population mean difference is greater than zero, meaning muscle with no treatment has more inflammation than muscle that has been massaged.

State the null and alternative hypothesis

Ho= Ha=

C.)Use StatKey or other technology to find the P-value from a randomization distribution.
P-value=?
Round your answer to three decimal places.

We want to test to see if the population mean difference \( \mu_D \) is greater than zero, meaning muscle with no treatment has more inflammation than muscle that has been massaged.

State the null and alternative hypotheses.

Use \( \mu \) instead of \( \mu_D \) to answer this question.

Equation Editor:

\[ = \quad \neq \quad < \quad > \quad \mu \quad \mu_1 \quad \mu_2 \quad p \quad p_1 \quad p_2 \quad 0 \quad \rho \quad \bar{x} \quad \bar{x}_1 \quad \bar{x}_2 \quad \hat{p} \quad \hat{p}_1 \quad \hat{p}_2 \quad r \]

Formulate:

\[ H_0: \quad \_ \quad \_ \quad \_ \quad \text{vs} \quad H_a: \quad \_ \quad \_ \quad \_ \]

**Does Massage Help Heal Muscles Strained by Exercise?**

After exercise, massage is often used to relieve pain, and a recent study¹ shows that it also may relieve inflammation and help muscles heal. In the study, eleven male participants who had just strenuously exercised had 10 minutes of massage on one quadricep and no treatment on the other, with treatment randomly assigned. After 2.5 hours, muscle biopsies were taken and production of the inflammatory cytokine interleukin-6 was measured relative to the resting level. The differences (control minus massage) are given in Table 1 below.

```
+-----+-----+-----+-----+-----+------+-----+-----+
| 0.6 | 4.7 | 3.8 | 0.4 | 1.5 | -1.2 | 2.8 | -0.4 | 1.4 | 3.5 | -2.8 |
+-----+-----+-----+-----+-----+------+-----+-----+
```

*Table 1: Inflammation in muscle: control minus massage*

¹ Data approximated from summary statistics in Crane, et al., "Massage Therapy Attenuates Inflammatory Signaling After Exercise-Induced Muscle Damage," *Science Translational Medicine*, 1 February 2012.

Click [here](#) to access StatKey.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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