K 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: PY H₁: P ▼ (Type integers or decimals. Do not round.) Identify the correlation coefficient, r. r= (Round to three decimal places as needed.) Identify the critical value(s). Correlation Results Correlation coeff, r: 0.969325 +0.2680855 Critical r P-value (two tailed): 0.000

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**Educational Analysis of Bear Weight and Chest Size Correlation**

In a study involving fifty-four wild bears, the subjects were anesthetized, and their weights and chest sizes were recorded. This data is used to determine if there's a linear correlation between the weight of the bears and their chest size. Additionally, we explore whether it's more efficient to measure chest size over weight for predicting the bear’s weight. The significance level for this evaluation is set at α = 0.05.

**Determine the Null and Alternative Hypotheses**

- Null Hypothesis (H₀): ρ = 0
- Alternative Hypothesis (H₁): ρ ≠ 0

**Correlation Results**

- **Correlation Coefficient (r):** 0.969325
- **Critical r:** ±0.2680855
- **P-value (two-tailed):** 0.000

**Analysis Steps:**

1. **Identify the Correlation Coefficient:** The correlation coefficient r is given as 0.969, indicating a strong positive linear relationship between the weights and chest sizes of the bears.

2. **Identify the Critical Value(s):** The critical value is ±0.2680855, under the null hypothesis for a two-tailed test.

3. **Statistical Significance:** With the p-value at 0.000, which is less than the significance level of 0.05, we reject the null hypothesis. This suggests that there is significant evidence to support a linear correlation between the bears' weights and chest sizes.

4. **Practical Implication:** Given the strong correlation, chest size can be used as a reliable predictor for bear weight in this context. This can be particularly handy in field situations where measuring weight directly is more challenging than measuring chest size.

This study underscores the importance of statistical analysis in wildlife research, facilitating better decision-making processes and resource management.
Transcribed Image Text:**Educational Analysis of Bear Weight and Chest Size Correlation** In a study involving fifty-four wild bears, the subjects were anesthetized, and their weights and chest sizes were recorded. This data is used to determine if there's a linear correlation between the weight of the bears and their chest size. Additionally, we explore whether it's more efficient to measure chest size over weight for predicting the bear’s weight. The significance level for this evaluation is set at α = 0.05. **Determine the Null and Alternative Hypotheses** - Null Hypothesis (H₀): ρ = 0 - Alternative Hypothesis (H₁): ρ ≠ 0 **Correlation Results** - **Correlation Coefficient (r):** 0.969325 - **Critical r:** ±0.2680855 - **P-value (two-tailed):** 0.000 **Analysis Steps:** 1. **Identify the Correlation Coefficient:** The correlation coefficient r is given as 0.969, indicating a strong positive linear relationship between the weights and chest sizes of the bears. 2. **Identify the Critical Value(s):** The critical value is ±0.2680855, under the null hypothesis for a two-tailed test. 3. **Statistical Significance:** With the p-value at 0.000, which is less than the significance level of 0.05, we reject the null hypothesis. This suggests that there is significant evidence to support a linear correlation between the bears' weights and chest sizes. 4. **Practical Implication:** Given the strong correlation, chest size can be used as a reliable predictor for bear weight in this context. This can be particularly handy in field situations where measuring weight directly is more challenging than measuring chest size. This study underscores the importance of statistical analysis in wildlife research, facilitating better decision-making processes and resource management.
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