### Decision Rule at 0.05 Significance Level**b. What is the decision rule?**To determine whether to reject the null hypothesis (H₀), use the F-statistic at a 0.05 significance level. - **Instruction:** Reject H₀ if F > [value].**Note:** Round your answer to 2 decimal places. The box adjacent to the instruction is provided for inputting the critical F-value needed to reject the null hypothesis. The postal service sorts mail as Priority Mail Express, Priority Mail, First-Class Mail, or Standard Mail. Over a period of 3 weeks, 18 of each type were mailed from the Network Distribution Center in Atlanta, Georgia, to Des Moines, Iowa. The total delivery time in days was recorded. Minitab was used to perform the ANOVA. The results follow:**ANOVA Table:**| Source | DF | SS | MS | F | P ||---------|----|------|------|------|------|| Factor | 3 | 2.05 | 0.68 | 2.13 | 0.104|| Error | 68 | 21.83| 0.32 | | || Total | 71 | 23.88| | | |**Levels with Descriptive Statistics:**| Level | N | Mean | StDev ||----------------------|----|------|-------|| Priority Mail Express| 18 | 2.928| 0.419 || Priority Mail | 18 | 3.066| 0.821 || First-Class Mail | 18 | 3.383| 0.586 || Standard Mail | 18 | 3.044| 0.301 |### Explanation of the Data:1. **Sources of Variation:** - **Factor:** Represents the different types of mail (Priority Mail Express, Priority Mail, First-Class Mail, Standard Mail). - **Error:** Reflects other sources of variation not accounted for by the factor. - **Total:** Combination of factor and error variations.2. **Statistics Calculated:** - **DF (Degrees of Freedom):** Number of levels minus one for factor, and total number of observations minus number of groups for error. - **SS (Sum of Squares):** Measures the total variability. - **MS (Mean Square):** SS divided by DF. - **F:** Ratio of MS factor to MS error, used to determine statistical significance. - **P-value:** Probability that the observed data would occur if the null hypothesis were true.3. **Interpretation:** - The **F-value** is 2.13, with a **P-value** of 0.104, indicating that there is no statistically significant difference at

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Description: ### Decision Rule at 0.05 Significance Level**b. What is the decision rule?**To determine whether to reject the null hypothesis (H₀), use the F-statistic at a 0.05 significance level. - **Instruction:** Reject H₀ if F > [value].**Note:** Round your

The degrees of freedom for factor is 3 and the degrees of freedom for error is 68.

Answered: . What is the decision rule? Use the…

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Statistics

. What is the decision rule? Use the O.05 significance level. (Round your answer to 2 decimal place Reject Ho if F>

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

### Decision Rule at 0.05 Significance Level

**b. What is the decision rule?**

To determine whether to reject the null hypothesis (H₀), use the F-statistic at a 0.05 significance level.

- **Instruction:** Reject H₀ if F > [value].

**Note:** Round your answer to 2 decimal places. The box adjacent to the instruction is provided for inputting the critical F-value needed to reject the null hypothesis.

The postal service sorts mail as Priority Mail Express, Priority Mail, First-Class Mail, or Standard Mail. Over a period of 3 weeks, 18 of each type were mailed from the Network Distribution Center in Atlanta, Georgia, to Des Moines, Iowa. The total delivery time in days was recorded. Minitab was used to perform the ANOVA. The results follow:

**ANOVA Table:**

| Source | DF | SS | MS | F | P |
|---------|----|------|------|------|------|
| Factor | 3 | 2.05 | 0.68 | 2.13 | 0.104|
| Error | 68 | 21.83| 0.32 | | |
| Total | 71 | 23.88| | | |

**Levels with Descriptive Statistics:**

| Level | N | Mean | StDev |
|----------------------|----|------|-------|
| Priority Mail Express| 18 | 2.928| 0.419 |
| Priority Mail | 18 | 3.066| 0.821 |
| First-Class Mail | 18 | 3.383| 0.586 |
| Standard Mail | 18 | 3.044| 0.301 |

### Explanation of the Data:

1. **Sources of Variation:**
- **Factor:** Represents the different types of mail (Priority Mail Express, Priority Mail, First-Class Mail, Standard Mail).
- **Error:** Reflects other sources of variation not accounted for by the factor.
- **Total:** Combination of factor and error variations.

2. **Statistics Calculated:**
- **DF (Degrees of Freedom):** Number of levels minus one for factor, and total number of observations minus number of groups for error.
- **SS (Sum of Squares):** Measures the total variability.
- **MS (Mean Square):** SS divided by DF.
- **F:** Ratio of MS factor to MS error, used to determine statistical significance.
- **P-value:** Probability that the observed data would occur if the null hypothesis were true.

3. **Interpretation:**
- The **F-value** is 2.13, with a **P-value** of 0.104, indicating that there is no statistically significant difference at

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