MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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7
### Study on the Correlation between Weight and Chest Size in Bears

**Objective:** 
Analyze whether there is a linear correlation between the weights and chest sizes of anesthetized bears and determine if chest size can predict weight.

---

**Experiment Description:**
Fifty-four wild bears were anesthetized, and their weights and chest sizes were measured and listed in a dataset. 

**Research Question:** 
Is there sufficient evidence to support the claim that there is a linear correlation between the weights of bears and their chest sizes? When measuring an anesthetized bear, is it easier to measure chest size than weight? If so, does it appear that a measured chest size can be used to predict the weight? The test uses a significance level of \(\alpha = 0.05\).

---

**Statistical Analysis:**

1. **Determine the Null and Alternative Hypotheses:**
    - **\(H_0\)**: \(\rho = 0\)
    - **\(H_1\)**: \(\rho \neq 0\)

2. **Correlation Coefficient:**
    - Identify the correlation coefficient, \(r\).
    - Given: \(r = 0.969394\)

3. **Critical Value(s):**
    - Identify the critical value(s) (rounded to three decimal places).
    - Two critical values: \(\pm 0.2680855\)

4. **Evaluating Sufficient Evidence for Linear Correlation:**
    - Determine if there is sufficient evidence to support the claim using the correlation test.
    - Given \(r = 0.969394\) which exceeds the critical value of 0.2680855.
    - Conclusion: Yes, because the absolute value of the test statistic exceeds the critical value.

---

**Practical Implications:**

When measuring an anesthetized bear, is it easier to measure chest size than weight? If so, does it appear that a measured chest size can be used to predict the weight?

- **Options for Practical Implications:**
    - **A.** Yes, it is easier to measure a chest size than weight because measuring weight would require lifting the bear onto the scale. The chest size could be used to predict weight because there is a linear correlation between the two.
    - **B.** Yes, it is easier to measure a chest size than weight because measuring weight would require lifting the bear onto the scale. The chest
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Transcribed Image Text:### Study on the Correlation between Weight and Chest Size in Bears **Objective:** Analyze whether there is a linear correlation between the weights and chest sizes of anesthetized bears and determine if chest size can predict weight. --- **Experiment Description:** Fifty-four wild bears were anesthetized, and their weights and chest sizes were measured and listed in a dataset. **Research Question:** Is there sufficient evidence to support the claim that there is a linear correlation between the weights of bears and their chest sizes? When measuring an anesthetized bear, is it easier to measure chest size than weight? If so, does it appear that a measured chest size can be used to predict the weight? The test uses a significance level of \(\alpha = 0.05\). --- **Statistical Analysis:** 1. **Determine the Null and Alternative Hypotheses:** - **\(H_0\)**: \(\rho = 0\) - **\(H_1\)**: \(\rho \neq 0\) 2. **Correlation Coefficient:** - Identify the correlation coefficient, \(r\). - Given: \(r = 0.969394\) 3. **Critical Value(s):** - Identify the critical value(s) (rounded to three decimal places). - Two critical values: \(\pm 0.2680855\) 4. **Evaluating Sufficient Evidence for Linear Correlation:** - Determine if there is sufficient evidence to support the claim using the correlation test. - Given \(r = 0.969394\) which exceeds the critical value of 0.2680855. - Conclusion: Yes, because the absolute value of the test statistic exceeds the critical value. --- **Practical Implications:** When measuring an anesthetized bear, is it easier to measure chest size than weight? If so, does it appear that a measured chest size can be used to predict the weight? - **Options for Practical Implications:** - **A.** Yes, it is easier to measure a chest size than weight because measuring weight would require lifting the bear onto the scale. The chest size could be used to predict weight because there is a linear correlation between the two. - **B.** Yes, it is easier to measure a chest size than weight because measuring weight would require lifting the bear onto the scale. The chest
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