need correlation coefficient ,test statistic , 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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![**Correlation Analysis of Bear Weight and Chest Size**
In a study involving fifty-four wild bears, both weight and chest size measurements were recorded after anesthetizing the animals. The aim is to determine if there's a linear correlation between a bear's weight and chest size, assessing whether chest size can potentially predict weight, especially when capturing the weight of an anesthetized bear might be challenging. The significance level for the analysis is set at \(\alpha = 0.05\).
**Determine the Null and Alternative Hypotheses:**
- Null Hypothesis, \( H_0: \rho = 0 \)
- Alternative Hypothesis, \( H_1: \rho \neq 0 \)
(*Note: Use integers or decimals without rounding when entering the hypotheses.*)
**Identify the Correlation Coefficient, \( r \):**
- \( r = \) [Enter your value here] (Round to three decimal places as needed.)
**Correlation Results:**
- **Correlation Coefficient \( r \):** \( 0.967366 \)
- **Critical \( r \):** \( \pm 0.2680885 \)
- **P-value (two-tailed):** \( 0.000 \)
The data suggests a significant correlation between the bears' chest sizes and weights, as indicated by the high correlation coefficient and a p-value less than 0.05.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F77cc80fa-a1ab-48f0-b2a0-996110f4bcad%2Fb1ced14f-8d36-4f9f-b5a9-56f20400809f%2Fewxm1cg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Correlation Analysis of Bear Weight and Chest Size**
In a study involving fifty-four wild bears, both weight and chest size measurements were recorded after anesthetizing the animals. The aim is to determine if there's a linear correlation between a bear's weight and chest size, assessing whether chest size can potentially predict weight, especially when capturing the weight of an anesthetized bear might be challenging. The significance level for the analysis is set at \(\alpha = 0.05\).
**Determine the Null and Alternative Hypotheses:**
- Null Hypothesis, \( H_0: \rho = 0 \)
- Alternative Hypothesis, \( H_1: \rho \neq 0 \)
(*Note: Use integers or decimals without rounding when entering the hypotheses.*)
**Identify the Correlation Coefficient, \( r \):**
- \( r = \) [Enter your value here] (Round to three decimal places as needed.)
**Correlation Results:**
- **Correlation Coefficient \( r \):** \( 0.967366 \)
- **Critical \( r \):** \( \pm 0.2680885 \)
- **P-value (two-tailed):** \( 0.000 \)
The data suggests a significant correlation between the bears' chest sizes and weights, as indicated by the high correlation coefficient and a p-value less than 0.05.
Transcribed Image Text:The task involves matching the values of the correlation coefficient, \( r \), to the corresponding scatterplots. The given values are 0.395, -0.995, -1, -0.78, and 0.78.
**Scatterplots Overview:**
- **Scatterplot 2:** This scatterplot features points that appear to be densely spaced without any noticeable trend, suggesting a near-zero correlation.
- **Scatterplot 3:** This scatterplot displays points aligned closely along a line with a negative slope, indicating a strong negative correlation.
- **Scatterplot 5:** Points in this scatterplot are more dispersed, following a general downward trend, which suggests a moderate negative correlation.
**Task Instructions:**
- Match each scatterplot (1 through 5) to one of the correlation coefficients provided.
- Use the dropdown menu next to each scatterplot to select the correct correlation value based on the plot's pattern.
**Considerations:**
- A perfect negative linear relationship is represented by \( r = -1 \).
- Strong negative correlations have values close to -1.
- Moderate correlations have values around ±0.5.
- Weak correlations have values closer to 0.
This task helps in understanding the relationship between data points and how the correlation coefficient reflects that relationship.
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