finding the test statistic and the P-value
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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I need help finding the test statistic and the P-value

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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