Please solve these subparts of the attached image question manually and using R-studio code, not an excel output. Thanks so much!a) We want to test if there is a difference in the mean heart rates for the three groups. Give the null hypothesisof this test.b) Does the data suggest that there is a difference among the three groups? Use α = 0.05.c) If there seems to be a difference, complete a Bonferroni pairwise test to determine which or if all the meansare different from each other. ### Study on the Effect of Pets in Stressful SituationsA study was conducted to examine the effect of pets on stress. Fifteen subjects were randomly assigned to each of three groups to do a stressful task alone (the control group), with a good friend present, or with their dog present. The subject’s mean heart rate (in beats per minute) during the task is one measure of the effect of stress. The data includes mean heart rates during stress with a pet (P), with a friend (F), and for the control group (C).#### Data Table:| Control | Friend | Pet ||---------|--------|-------|| 80.369 | 99.692 | 69.169|| 87.446 | 83.4 | 70.169|| 90.015 | 102.154| 75.985|| 99.046 | 80.277 | 86.446|| 75.477 | 88.015 | 68.862|| 87.231 | 92.492 | 64.169|| 91.754 | 91.354 | 97.538|| 87.785 | 100.877| 85 || 77.8 | 101.062| 72.262|| 62.646 | 81.6 | 58.692|| 84.738 | 89.815 | 79.662|| 84.877 | 98.2 | 69.231|| 73.277 | 76.908 | 69.538|| 84.523 | 86.985 | 70.077|| 70.877 | 97.046 | 65.446|#### Analysis:- **Control Group:** This group shows a range of heart rates with some reaching as high as 99.046 bpm.- **Friend Group:** Heart rates in this group seem to vary widely, with some rates above 100 bpm.- **Pet Group:** This group generally shows lower heart rates, suggesting a potential calming effect of having a pet present during stressful tasks.This dataset provides insights into how the presence of different companions can affect physiological responses such as heart rate during stress.

Given data: Control Friend Pet 80.369 99.692 69.169 87.446 83.4 70.169 90.015 102.154…

Answered: Please solve these subparts of the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Please solve these subparts of the attached image question manually and using R-studio code, not an excel output. Thanks so much!

a) We want to test if there is a difference in the mean heart rates for the three groups. Give the null hypothesis
of this test.

b) Does the data suggest that there is a difference among the three groups? Use α = 0.05.
c) If there seems to be a difference, complete a Bonferroni pairwise test to determine which or if all the means
are different from each other.

### Study on the Effect of Pets in Stressful Situations

A study was conducted to examine the effect of pets on stress. Fifteen subjects were randomly assigned to each of three groups to do a stressful task alone (the control group), with a good friend present, or with their dog present. The subject’s mean heart rate (in beats per minute) during the task is one measure of the effect of stress. The data includes mean heart rates during stress with a pet (P), with a friend (F), and for the control group (C).

#### Data Table:

| Control | Friend | Pet |
|---------|--------|-------|
| 80.369 | 99.692 | 69.169|
| 87.446 | 83.4 | 70.169|
| 90.015 | 102.154| 75.985|
| 99.046 | 80.277 | 86.446|
| 75.477 | 88.015 | 68.862|
| 87.231 | 92.492 | 64.169|
| 91.754 | 91.354 | 97.538|
| 87.785 | 100.877| 85 |
| 77.8 | 101.062| 72.262|
| 62.646 | 81.6 | 58.692|
| 84.738 | 89.815 | 79.662|
| 84.877 | 98.2 | 69.231|
| 73.277 | 76.908 | 69.538|
| 84.523 | 86.985 | 70.077|
| 70.877 | 97.046 | 65.446|

#### Analysis:

- **Control Group:** This group shows a range of heart rates with some reaching as high as 99.046 bpm.
- **Friend Group:** Heart rates in this group seem to vary widely, with some rates above 100 bpm.
- **Pet Group:** This group generally shows lower heart rates, suggesting a potential calming effect of having a pet present during stressful tasks.

This dataset provides insights into how the presence of different companions can affect physiological responses such as heart rate during stress.

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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