Step 1: State the hypotheses.(Select A, B, or C)Hypotheses = Step 2: State the critical values.df = t-critical value = +/- (use 3 places to the right of the decimal point)Step 3: Compute the test statistic: Summary StatisticsPooled Variance: sP2 = (Use 3 dec. places)Pooled Standard Deviation: sP = (Use 3 dec. places) ### Statistical Hypothesis Testing: Comparing Two Means**Given Data:**- **Pessimistic Group:** - Sample size (n) = 10 - Mean (M) = 2.9 - Sum of Squares (SS) = 40.9 - Variance (\(s^2\)) = 4.54- **Optimistic Group:** - Sample size (n) = 10 - Mean (M) = 6.8 - Sum of Squares (SS) = 25.6 - Variance (\(s^2\)) = 2.84### Step-by-Step Process**Step 1: State the Hypotheses. (Select A, B, or C)**- **(A)** - \(H_0: \mu_1 - \mu_2 = 0\) - \(H_1: \mu_1 - \mu_2 \neq 0\)- **(B)** - \(H_0: \mu_1 \neq \mu_2\) - \(H_1: \mu_1 = \mu_2\)- **(C)** - \(H_0: \mu_1 - \mu_2 \neq 0\) - \(H_1: \mu_1 - \mu_2 = 0\)*Hypotheses:* [ ] (Select one option from A, B, or C)**Step 2: State the Critical Values.**- Degrees of Freedom (\(df\)): [ ] - t-critical value: \(\pm\) [ ] *(Use three decimal places)***Step 3: Compute the Test Statistic: Summary Statistics**- **Pooled Variance (\(s^2_p\))** = [ ] *(Use three decimal places)*- **Pooled Standard Deviation (\(s_p\))** = [ ] *(Use three decimal places)*This template guides you through the process of setting up hypotheses, determining critical values for hypothesis testing, and calculating test statistics using summary statistics. **Research Study on Recycling Habits and Attitudes****Q21. Individual Actions and Environmental Health**Individual actions can significantly impact the overall health of our planet. A researcher focused on evaluating environmentally friendly behaviors examined how often people recycle (per month), based on whether they have a predominantly optimistic or pessimistic attitude toward eco-friendly behaviors. This is a hypothetical study, and the results are shown in the table below. Use this data to test the hypothesis that the number of complaints changed after implementing a new policy, applying a two-tailed test with a significance level of α = .05.**Recycling Frequency Based on Attitude**| Pessimistic | Optimistic ||-------------|------------|| 3 | 4 || 0 | 9 || 4 | 6 || 2 | 8 || 1 | 9 || 6 | 5 || 5 | 8 || 0 | 6 || 5 | 7 |**Statistical Data Summary**- **Pessimistic Group:** - Number of participants (n) = 10 - Mean (M) = 2.9 - Sum of Squares (SS) = 40.9 - Variance (s²) = 4.54- **Optimistic Group:** - Number of participants (n) = 10 - Mean (M) = 6.8 - Sum of Squares (SS) = 25.6 - Variance (s²) = 2.84This study aims to explore whether an optimistic attitude correlates with increased recycling behavior, which could indicate fewer complaints about environmental initiatives. The analysis uses a rigorous statistical approach to draw meaningful conclusions.

Given Data : For Sample 1 x̄1 = 2.9 s1 = √4.54 = 2.1307 n1 = 10 For…

Pessimistic: n = 10, M = 2.9, SS = 40.9, s? = 4.54 Optimistic: n = 10, M = 6.8, SS = 25.6, s? = 2.84 %3D %3D %3D Step 1: State the hypotheses. (Select A, B, or C) (A) (B) (C) HO: μι- μ2#0 H1: μι- μ2 = 0 HO: µ1 # µ2 H0: μι-μ2 = 0 Η 1: μι- μ2 + 0 H1: μι- μ2 Hypotheses Step 2: State the critical values. df = t-critical value = +/- (use 3 places to the right of the decimal point) Step 3: Compute the test statistic: Summary Statistics Pooled Variance: Sp2 = (Use 3 dec. places) Pooled Standard Deviation: Sp = (Use 3 dec. places)

Pessimistic: n = 10, M = 2.9, SS = 40.9, s? = 4.54 Optimistic: n = 10, M = 6.8, SS = 25.6, s? = 2.84 %3D %3D %3D Step 1: State the hypotheses. (Select A, B, or C) (A) (B) (C) HO: μι- μ2#0 H1: μι- μ2 = 0 HO: µ1 # µ2 H0: μι-μ2 = 0 Η 1: μι- μ2 + 0 H1: μι- μ2 Hypotheses Step 2: State the critical values. df = t-critical value = +/- (use 3 places to the right of the decimal point) Step 3: Compute the test statistic: Summary Statistics Pooled Variance: Sp2 = (Use 3 dec. places) Pooled Standard Deviation: Sp = (Use 3 dec. places)

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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Question

Step 1: State the hypotheses.
(Select A, B, or C)

Hypotheses =

Step 2: State the critical values.

df =

t-critical value = +/-
(use 3 places to the right of the decimal point)

Step 3: Compute the test statistic: Summary Statistics

Pooled Variance: s_P² =
(Use 3 dec. places)

Pooled Standard Deviation: s_P =
(Use 3 dec. places)

### Statistical Hypothesis Testing: Comparing Two Means

**Given Data:**
- **Pessimistic Group:**
- Sample size (n) = 10
- Mean (M) = 2.9
- Sum of Squares (SS) = 40.9
- Variance (\(s^2\)) = 4.54
- **Optimistic Group:**
- Sample size (n) = 10
- Mean (M) = 6.8
- Sum of Squares (SS) = 25.6
- Variance (\(s^2\)) = 2.84

### Step-by-Step Process

**Step 1: State the Hypotheses. (Select A, B, or C)**

- **(A)**
- \(H_0: \mu_1 - \mu_2 = 0\)
- \(H_1: \mu_1 - \mu_2 \neq 0\)
- **(B)**
- \(H_0: \mu_1 \neq \mu_2\)
- \(H_1: \mu_1 = \mu_2\)
- **(C)**
- \(H_0: \mu_1 - \mu_2 \neq 0\)
- \(H_1: \mu_1 - \mu_2 = 0\)

*Hypotheses:* [ ] (Select one option from A, B, or C)

**Step 2: State the Critical Values.**

- Degrees of Freedom (\(df\)): [ ]
- t-critical value: \(\pm\) [ ]
*(Use three decimal places)*

**Step 3: Compute the Test Statistic: Summary Statistics**

- **Pooled Variance (\(s^2_p\))** = [ ]
*(Use three decimal places)*

- **Pooled Standard Deviation (\(s_p\))** = [ ]
*(Use three decimal places)*

This template guides you through the process of setting up hypotheses, determining critical values for hypothesis testing, and calculating test statistics using summary statistics.

**Research Study on Recycling Habits and Attitudes**

**Q21. Individual Actions and Environmental Health**

Individual actions can significantly impact the overall health of our planet. A researcher focused on evaluating environmentally friendly behaviors examined how often people recycle (per month), based on whether they have a predominantly optimistic or pessimistic attitude toward eco-friendly behaviors. This is a hypothetical study, and the results are shown in the table below. Use this data to test the hypothesis that the number of complaints changed after implementing a new policy, applying a two-tailed test with a significance level of α = .05.

**Recycling Frequency Based on Attitude**

| Pessimistic | Optimistic |
|-------------|------------|
| 3 | 4 |
| 0 | 9 |
| 4 | 6 |
| 2 | 8 |
| 1 | 9 |
| 6 | 5 |
| 5 | 8 |
| 0 | 6 |
| 5 | 7 |

**Statistical Data Summary**

- **Pessimistic Group:**
- Number of participants (n) = 10
- Mean (M) = 2.9
- Sum of Squares (SS) = 40.9
- Variance (s²) = 4.54

- **Optimistic Group:**
- Number of participants (n) = 10
- Mean (M) = 6.8
- Sum of Squares (SS) = 25.6
- Variance (s²) = 2.84

This study aims to explore whether an optimistic attitude correlates with increased recycling behavior, which could indicate fewer complaints about environmental initiatives. The analysis uses a rigorous statistical approach to draw meaningful conclusions.

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