finding the test statistic and the P-value

MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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I need help finding the test statistic and the P-value

**Educational Resource: Analyzing Correlation Between Lemon Imports and Crash Fatality Rates**

**Data Analysis Overview:**

The table below presents annual data over various years, with two key variables:
- **Lemon Imports** (in metric tons)
- **Crash Fatality Rate** (per 100,000 population)

| Lemon Imports | Crash Fatality Rate |
|---------------|---------------------|
| 228           | 15.9                |
| 266           | 15.7                |
| 358           | 15.5                |
| 483           | 15.3                |
| 534           | 14.8                |

**Research Objective:**

Evaluate the relationship between lemon imports and crash fatality rates by calculating the linear correlation coefficient \( r \). Determine the statistical significance using a significance level of \( \alpha = 0.05 \). Explore whether there is a meaningful correlation which implies that lemon imports might affect crash fatality rates.

**Hypotheses:**

Identify the null and alternative hypotheses for statistical testing:
- \( H_0: \rho = 0 \) (No correlation)
- \( H_1: \rho \neq 0 \) (Some correlation)

**Scatterplot Construction:**

Selected Scatterplot (Option C) Visual Details:
- The x-axis represents Lemon Imports.
- The y-axis represents the Crash Fatality Rate.
- Points on the scatterplot illustrate a downward trend, suggesting a negative relationship.

**Statistical Analysis:**

- The computed linear correlation coefficient is \( r = -0.953 \).
  - This value suggests a strong negative correlation between lemon imports and crash fatality rates.

**Conclusion:**

The analysis demonstrates a strong inverse correlation, which statistically suggests a decrease in crash fatality rates with an increase in lemon imports. However, correlation does not imply causation; thus, no direct conclusion can be drawn that lemon imports cause a reduction in crash fatalities. The correlation might be coincidental or influenced by external variables.
Transcribed Image Text:**Educational Resource: Analyzing Correlation Between Lemon Imports and Crash Fatality Rates** **Data Analysis Overview:** The table below presents annual data over various years, with two key variables: - **Lemon Imports** (in metric tons) - **Crash Fatality Rate** (per 100,000 population) | Lemon Imports | Crash Fatality Rate | |---------------|---------------------| | 228 | 15.9 | | 266 | 15.7 | | 358 | 15.5 | | 483 | 15.3 | | 534 | 14.8 | **Research Objective:** Evaluate the relationship between lemon imports and crash fatality rates by calculating the linear correlation coefficient \( r \). Determine the statistical significance using a significance level of \( \alpha = 0.05 \). Explore whether there is a meaningful correlation which implies that lemon imports might affect crash fatality rates. **Hypotheses:** Identify the null and alternative hypotheses for statistical testing: - \( H_0: \rho = 0 \) (No correlation) - \( H_1: \rho \neq 0 \) (Some correlation) **Scatterplot Construction:** Selected Scatterplot (Option C) Visual Details: - The x-axis represents Lemon Imports. - The y-axis represents the Crash Fatality Rate. - Points on the scatterplot illustrate a downward trend, suggesting a negative relationship. **Statistical Analysis:** - The computed linear correlation coefficient is \( r = -0.953 \). - This value suggests a strong negative correlation between lemon imports and crash fatality rates. **Conclusion:** The analysis demonstrates a strong inverse correlation, which statistically suggests a decrease in crash fatality rates with an increase in lemon imports. However, correlation does not imply causation; thus, no direct conclusion can be drawn that lemon imports cause a reduction in crash fatalities. The correlation might be coincidental or influenced by external variables.
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