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Fifty-four wild bears were anesthetized, and then their weights and 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 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? Use a significance level of a = 0.05. Determine the null and alternative hypotheses. Ho: P H₁: PY (Type integers or decimals. Do not round.) Correlation Results Correlation coeff, r: 0.978311 Critical r ±0.2680855 P-value (two tailed): 0.000

Fifty-four wild bears were anesthetized, and then their weights and 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 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? Use a significance level of a = 0.05. Determine the null and alternative hypotheses. Ho: P H₁: PY (Type integers or decimals. Do not round.) Correlation Results Correlation coeff, r: 0.978311 Critical r ±0.2680855 P-value (two tailed): 0.000

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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Fifty-four wild bears were anesthetized, and then their weights and 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 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? Use a significance level of a = 0.05 Question: Determine the null and alternative hypotheses
**Analysis of Linear Correlation between Weights and Chest Sizes of Wild Bears** A study was conducted involving fifty-four wild bears, which were anesthetized for measurements. The weights and chest sizes of these bears were recorded in a dataset. The objective was to determine if there is sufficient evidence to support the claim of a linear correlation between the weights and chest sizes of these bears. The question arises whether measuring an anesthetized bear's chest size is easier and possibly used as a predictor for its weight. A significance level of \(\alpha = 0.05\) was used in this analysis. **Correlation Results:** - **Correlation coefficient (\(r\))**: 0.978311 - **Critical \(r\)**: ±0.2668055 - **P-value (two-tailed)**: 0.000 The results reveal a high positive correlation coefficient (\(r = 0.978311\)), suggesting a strong linear relationship between the chest sizes and weights of these bears. The critical \(r\) value indicates the threshold for significance, and the P-value of 0.000, being lower than the significance level of 0.05, provides strong evidence to reject the null hypothesis of no correlation. **Hypothesis Testing:** - **Null Hypothesis (\(H_0\))**: \(\rho = 0\) (There is no linear correlation between weights and chest sizes) - **Alternative Hypothesis (\(H_1\))**: \(\rho \neq 0\) (There is a linear correlation between weights and chest sizes) The findings support the alternative hypothesis, indicating a significant linear correlation. Therefore, measured chest size can be used to predict the bear's weight effectively.
Transcribed Image Text:**Analysis of Linear Correlation between Weights and Chest Sizes of Wild Bears** A study was conducted involving fifty-four wild bears, which were anesthetized for measurements. The weights and chest sizes of these bears were recorded in a dataset. The objective was to determine if there is sufficient evidence to support the claim of a linear correlation between the weights and chest sizes of these bears. The question arises whether measuring an anesthetized bear's chest size is easier and possibly used as a predictor for its weight. A significance level of \(\alpha = 0.05\) was used in this analysis. **Correlation Results:** - **Correlation coefficient (\(r\))**: 0.978311 - **Critical \(r\)**: ±0.2668055 - **P-value (two-tailed)**: 0.000 The results reveal a high positive correlation coefficient (\(r = 0.978311\)), suggesting a strong linear relationship between the chest sizes and weights of these bears. The critical \(r\) value indicates the threshold for significance, and the P-value of 0.000, being lower than the significance level of 0.05, provides strong evidence to reject the null hypothesis of no correlation. **Hypothesis Testing:** - **Null Hypothesis (\(H_0\))**: \(\rho = 0\) (There is no linear correlation between weights and chest sizes) - **Alternative Hypothesis (\(H_1\))**: \(\rho \neq 0\) (There is a linear correlation between weights and chest sizes) The findings support the alternative hypothesis, indicating a significant linear correlation. Therefore, measured chest size can be used to predict the bear's weight effectively.
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