Based on the attached Table 2 and 3:1) How would you describe the result of t = -1.45 in this study?2) Which t test statistic listed in Table 3 represents the smallest relative difference between the pretest and 3 months? Is it statistically significant? What does this result mean?3) What are the assumptions for conducting a t-test for dependent groups? Which of these assumptions do you think were met by this study? **Table 2: Program Effects on Cardiovascular Risk Factors**This table summarizes the effects of a specific program on various cardiovascular risk factors over time, assessed at pretest, 3 months, and 6 months. Each variable is represented with its mean (M) and standard deviation (SD) at each time point. The effectiveness of the program over the specified periods is evaluated using paired t-tests, with significance denoted for p-values less than 0.05.- **Total Risk Score** - Pretest: M = 20.1 (SD = 4.5) - 3 months: M = 16.8 (SD = 3.2), Paired t = 4.14* - 6 months: M = 18.1 (SD = 4.0), Paired t = 2.56*- **Cholesterol** - Pretest: M = 200.2 (SD = 29.1) - 3 months: M = 189.6 (SD = 25.3), Paired t = 2.03* - 6 months: M = 192.7 (SD = 22.1), Paired t = 1.73- **Triglyceride** - Pretest: M = 164.2 (SD = 42.0) - 3 months: M = 150.4 (SD = 44.1), Paired t = 2.58* - 6 months: M = 142.9 (SD = 35.5), Paired t = 2.20*- **Body Mass Index (BMI)** - Pretest: M = 22.7 (SD = 3.0) - 3 months: M = 22.1 (SD = 3.0), Paired t = 3.44* - 6 months: M = 22.9 (SD = 3.0), Paired t = -0.80- **Systolic Blood Pressure (BP)** - Pretest: M = 121.7 (SD = 14.6) - 3 months: M = 117.2 (SD = 12.3), Paired t = 1.57 - 6 months: M = 115. **Table 3: Program Effects on Health Behaviors**This table presents the effects of the program on various health behaviors at pretest, 3 months, and 6 months. The data includes means (M) and standard deviations (SD) for each health behavior, as well as paired t-test results comparing pretest with 3-month and 6-month measures.| Variable | Pretest M (SD) | 3 Months M (SD) | Paired t$^a$ | 6 Months M (SD) | Paired t$^b$ ||------------------------|----------------|-----------------|---------------|-----------------|----------------|| Total Health Behavior | 66.3 (8.1) | 69.7 (5.0) | -3.02* | 68.1 (5.1) | -1.34 || Health Responsibility | 2.19 (0.5) | 2.13 (0.3) | 1.03 | 2.29 (0.3) | -1.99 || Exercise | 1.88 (0.3) | 2.58 (0.3) | -7.75* | 2.29 (0.4) | -3.93* || Diet Behavior | 3.41 (0.3) | 3.47 (0.2) | -0.93 | 3.26 (0.3) | 2.00 || Stress Management | 2.39 (0.4) | 2.44 (0.3) | -0.65 | 2.45 (0.3) | -0.70 || Smoking Behavior | 2.85 (0.8) | 2.92 (0.8) | -1.45 | 3.01 (0.7) | -0.96 |- *p < 0.05**Notes:**- $^a$Paired t-test results between the pretest and 3-month measures.- $^b$Paired t-test results between the pretest and 6-month measures.**Explanation:**- Significant improvements were

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Description: Based on the attached Table 2 and 3:1) How would you describe the result of t = -1.45 in this study?2) Which t test statistic listed in Table 3 represents the smallest relative difference between the pretest and 3 months? Is it statistically signific

Part 1: In table 3, the value of the test-statistics as t = -1.45 shows that within the 3 months…

Answered: Based on the attached Table 2 and 3:…

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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Based on the attached Table 2 and 3:

1) How would you describe the result of t = -1.45 in this study?

2) Which t test statistic listed in Table 3 represents the smallest relative difference between the pretest and 3 months? Is it statistically significant? What does this result mean?

3) What are the assumptions for conducting a t-test for dependent groups? Which of these assumptions do you think were met by this study?

**Table 2: Program Effects on Cardiovascular Risk Factors**

This table summarizes the effects of a specific program on various cardiovascular risk factors over time, assessed at pretest, 3 months, and 6 months. Each variable is represented with its mean (M) and standard deviation (SD) at each time point. The effectiveness of the program over the specified periods is evaluated using paired t-tests, with significance denoted for p-values less than 0.05.

- **Total Risk Score**
- Pretest: M = 20.1 (SD = 4.5)
- 3 months: M = 16.8 (SD = 3.2), Paired t = 4.14*
- 6 months: M = 18.1 (SD = 4.0), Paired t = 2.56*

- **Cholesterol**
- Pretest: M = 200.2 (SD = 29.1)
- 3 months: M = 189.6 (SD = 25.3), Paired t = 2.03*
- 6 months: M = 192.7 (SD = 22.1), Paired t = 1.73

- **Triglyceride**
- Pretest: M = 164.2 (SD = 42.0)
- 3 months: M = 150.4 (SD = 44.1), Paired t = 2.58*
- 6 months: M = 142.9 (SD = 35.5), Paired t = 2.20*

- **Body Mass Index (BMI)**
- Pretest: M = 22.7 (SD = 3.0)
- 3 months: M = 22.1 (SD = 3.0), Paired t = 3.44*
- 6 months: M = 22.9 (SD = 3.0), Paired t = -0.80

- **Systolic Blood Pressure (BP)**
- Pretest: M = 121.7 (SD = 14.6)
- 3 months: M = 117.2 (SD = 12.3), Paired t = 1.57
- 6 months: M = 115.

**Table 3: Program Effects on Health Behaviors**

This table presents the effects of the program on various health behaviors at pretest, 3 months, and 6 months. The data includes means (M) and standard deviations (SD) for each health behavior, as well as paired t-test results comparing pretest with 3-month and 6-month measures.

| Variable | Pretest M (SD) | 3 Months M (SD) | Paired t$^a$ | 6 Months M (SD) | Paired t$^b$ |
|------------------------|----------------|-----------------|---------------|-----------------|----------------|
| Total Health Behavior | 66.3 (8.1) | 69.7 (5.0) | -3.02* | 68.1 (5.1) | -1.34 |
| Health Responsibility | 2.19 (0.5) | 2.13 (0.3) | 1.03 | 2.29 (0.3) | -1.99 |
| Exercise | 1.88 (0.3) | 2.58 (0.3) | -7.75* | 2.29 (0.4) | -3.93* |
| Diet Behavior | 3.41 (0.3) | 3.47 (0.2) | -0.93 | 3.26 (0.3) | 2.00 |
| Stress Management | 2.39 (0.4) | 2.44 (0.3) | -0.65 | 2.45 (0.3) | -0.70 |
| Smoking Behavior | 2.85 (0.8) | 2.92 (0.8) | -1.45 | 3.01 (0.7) | -0.96 |

- *p < 0.05

**Notes:**
- $^a$Paired t-test results between the pretest and 3-month measures.
- $^b$Paired t-test results between the pretest and 6-month measures.

**Explanation:**

- Significant improvements were

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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