Follow PHANTOMS acronym ## PHANTOMS Framework for Statistical Analysis ### P - **Parameter Statement**Define the parameter of interest in the population. This might include the population mean, population proportion, or another measure you are estimating or testing about.### H - **Hypotheses**State the null hypothesis (H₀) and the alternative hypothesis (H₁). The null hypothesis usually represents no effect or no difference, while the alternative hypothesis suggests the presence of an effect or difference.### A - **Assumptions & Conditions**List and check the assumptions and conditions necessary for the test to be valid. This may include normality, independence, random sampling, and equal variances among groups.### N - **Name the Test**Specify the statistical test that will be used to analyze the data, such as a t-test, chi-square test, ANOVA, etc.### T - **Test Statistic**Calculate the test statistic based on your sample data. This could be a z-score, t-score, F-value, chi-square value, or another relevant metric.### O - **Obtain the P-Value**Determine the p-value corresponding to the test statistic. This p-value helps to decide whether to reject the null hypothesis.### M - **Make a Decision about the Null Hypothesis**Based on the p-value and the significance level (usually α = 0.05), decide whether to reject or fail to reject the null hypothesis. ### S - **State Your Conclusion About the Claim**Clearly state the conclusion in context of the hypothesis test. Summarize the findings, including whether there is sufficient evidence to support the alternative hypothesis.This systematic framework helps in organizing and conducting hypothesis testing effectively, ensuring that all key elements are addressed. ### Study on Waistline Reduction Through ExerciseTo evaluate the effectiveness of an exercise regimen, a physical therapist conducted a randomized study involving 10 women. Their waistlines were measured before and 8 weeks after participating in a rigorous exercise program. The data collected is as follows:#### Waistline Measurements (in inches)| Participant | Waistline Before | Waistline After ||-------------|------------------|----------------|| 1 | 23.5 | 19.75 || 2 | 18.5 | 19.25 || 3 | 21.5 | 21.75 || 4 | 24 | 22.5 || 5 | 25 | 25 || 6 | 19.75 | 19.5 || 7 | 35 | 34.25 || 8 | 36.5 | 35 || 9 | 52 | 51.5 || 10 | 30 | 31 |### Statistical Significance Test- **Objective:** To determine if there is significant evidence at the 0.05 level of significance to show that the waistline decreased after the rigorous exercise program.- **Method:** Any standard statistical method can be used, such as the paired sample t-test, to compare the waistline measurements before and after the program.**Instructions for Evaluation:**1. Compute the differences in waistline measurements before and after the exercise program for each participant.2. Calculate the mean and standard deviation of these differences.3. Perform the paired sample t-test.4. Compare the p-value obtained from the test with the significance level of 0.05. If the p-value is less than 0.05, reject the null hypothesis that there is no difference in waistline measurements, suggesting that the exercise program was effective in reducing waistline measurements. By conducting this analysis, one can determine whether the exercise regimen statistically significantly reduced waistlines in the study group.

The following information has been provided: Sample 1 = Waist Line Before Sample 2 = Waist Line…

To learn the effectiveness of an exercise regimen, a physical therapist randomly selects 10 women to participate in a study. She measures their waistlines before a rigorous exercise program and 8 weeks after the program begins and obtains the following data: Waistline Before 23.5 18.5 21.5 24 25 19.75 35 36.5 52 30 Waistline After 19.75 19.25 21.75 22.5 25 19.5 34.25 35 51.5 31

To learn the effectiveness of an exercise regimen, a physical therapist randomly selects 10 women to participate in a study. She measures their waistlines before a rigorous exercise program and 8 weeks after the program begins and obtains the following data: Waistline Before 23.5 18.5 21.5 24 25 19.75 35 36.5 52 30 Waistline After 19.75 19.25 21.75 22.5 25 19.5 34.25 35 51.5 31

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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Concept explainers

Power Operation

Power operation is topic of algebra in Math. It is use to represent repeated multiplication. Very big number and very small number can be easily express using power operation. Power operation is useful in many fields. In space engineering, it helps in representing the distance or size of particular heavenly body. In medical field, it is used to represent very small size. In medical field it helps to mention size of bacteria or virus.

Exponents

The exponent or power or index of a variable/number is the number of times that variable/number is multiplied by itself.

Question

Follow PHANTOMS acronym

## PHANTOMS Framework for Statistical Analysis

### P - **Parameter Statement**
Define the parameter of interest in the population. This might include the population mean, population proportion, or another measure you are estimating or testing about.

### H - **Hypotheses**
State the null hypothesis (H₀) and the alternative hypothesis (H₁). The null hypothesis usually represents no effect or no difference, while the alternative hypothesis suggests the presence of an effect or difference.

### A - **Assumptions & Conditions**
List and check the assumptions and conditions necessary for the test to be valid. This may include normality, independence, random sampling, and equal variances among groups.

### N - **Name the Test**
Specify the statistical test that will be used to analyze the data, such as a t-test, chi-square test, ANOVA, etc.

### T - **Test Statistic**
Calculate the test statistic based on your sample data. This could be a z-score, t-score, F-value, chi-square value, or another relevant metric.

### O - **Obtain the P-Value**
Determine the p-value corresponding to the test statistic. This p-value helps to decide whether to reject the null hypothesis.

### M - **Make a Decision about the Null Hypothesis**
Based on the p-value and the significance level (usually α = 0.05), decide whether to reject or fail to reject the null hypothesis.

### S - **State Your Conclusion About the Claim**
Clearly state the conclusion in context of the hypothesis test. Summarize the findings, including whether there is sufficient evidence to support the alternative hypothesis.

This systematic framework helps in organizing and conducting hypothesis testing effectively, ensuring that all key elements are addressed.

### Study on Waistline Reduction Through Exercise

To evaluate the effectiveness of an exercise regimen, a physical therapist conducted a randomized study involving 10 women. Their waistlines were measured before and 8 weeks after participating in a rigorous exercise program. The data collected is as follows:

#### Waistline Measurements (in inches)

| Participant | Waistline Before | Waistline After |
|-------------|------------------|----------------|
| 1 | 23.5 | 19.75 |
| 2 | 18.5 | 19.25 |
| 3 | 21.5 | 21.75 |
| 4 | 24 | 22.5 |
| 5 | 25 | 25 |
| 6 | 19.75 | 19.5 |
| 7 | 35 | 34.25 |
| 8 | 36.5 | 35 |
| 9 | 52 | 51.5 |
| 10 | 30 | 31 |

### Statistical Significance Test

- **Objective:** To determine if there is significant evidence at the 0.05 level of significance to show that the waistline decreased after the rigorous exercise program.
- **Method:** Any standard statistical method can be used, such as the paired sample t-test, to compare the waistline measurements before and after the program.

**Instructions for Evaluation:**
1. Compute the differences in waistline measurements before and after the exercise program for each participant.
2. Calculate the mean and standard deviation of these differences.
3. Perform the paired sample t-test.
4. Compare the p-value obtained from the test with the significance level of 0.05. If the p-value is less than 0.05, reject the null hypothesis that there is no difference in waistline measurements, suggesting that the exercise program was effective in reducing waistline measurements.

By conducting this analysis, one can determine whether the exercise regimen statistically significantly reduced waistlines in the study group.

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