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Fifty-four wild bears were anesthetized, and then their weights and Correlation Results chest sizes were measured and listed in a data set. Results are shown in the accompanying display. 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 Correlation coeff, r: Critical r:

Fifty-four wild bears were anesthetized, and then their weights and Correlation Results chest sizes were measured and listed in a data set. Results are shown in the accompanying display. 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 Correlation coeff, r: Critical r:

MATLAB: An Introduction with Applications
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 coefficient r= What is the critical value R=
**Educational Website Content** **Study on Wild Bears: Weight and Chest Size Correlation** Fifty-four wild bears were anesthetized, and their weights and chest sizes were measured and listed in a dataset. We are examining whether there is sufficient evidence to support the claim that there is a linear correlation between the weights of bears and their chest sizes. This analysis helps determine if chest size can be a predictor of weight when direct weight measurement is not feasible. **Research Question:** When measuring an anesthetized bear, is it easier to measure chest size than weight? If so, can a measured chest size be used to predict the weight? **Significance Level:** α = 0.05 **Correlation Results:** - **Correlation Coefficient (r):** 0.968963 - **Critical r:** ± 0.2680855 - **P-value (two-tailed):** 0.000 **Hypotheses:** - **Null Hypothesis (H₀):** ρ = 0 (There is no linear correlation between chest size and weight.) - **Alternative Hypothesis (H₁):** ρ ≠ 0 (There is a linear correlation between chest size and weight.) These results suggest that there is a strong positive correlation between chest size and weight, with the correlation coefficient (r = 0.968963) indicating a strong linear relationship. The p-value (0.000) is less than the significance level, suggesting that we reject the null hypothesis in favor of the alternative hypothesis. Hence, it appears that chest size can be used to predict weight in wild bears.
Transcribed Image Text:**Educational Website Content** **Study on Wild Bears: Weight and Chest Size Correlation** Fifty-four wild bears were anesthetized, and their weights and chest sizes were measured and listed in a dataset. We are examining whether there is sufficient evidence to support the claim that there is a linear correlation between the weights of bears and their chest sizes. This analysis helps determine if chest size can be a predictor of weight when direct weight measurement is not feasible. **Research Question:** When measuring an anesthetized bear, is it easier to measure chest size than weight? If so, can a measured chest size be used to predict the weight? **Significance Level:** α = 0.05 **Correlation Results:** - **Correlation Coefficient (r):** 0.968963 - **Critical r:** ± 0.2680855 - **P-value (two-tailed):** 0.000 **Hypotheses:** - **Null Hypothesis (H₀):** ρ = 0 (There is no linear correlation between chest size and weight.) - **Alternative Hypothesis (H₁):** ρ ≠ 0 (There is a linear correlation between chest size and weight.) These results suggest that there is a strong positive correlation between chest size and weight, with the correlation coefficient (r = 0.968963) indicating a strong linear relationship. The p-value (0.000) is less than the significance level, suggesting that we reject the null hypothesis in favor of the alternative hypothesis. Hence, it appears that chest size can be used to predict weight in wild bears.
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