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Yearling 12 31 33 10 34 11 Adult 27 Column Total 92 166 55 51 60 A USE SALT Use a chi-square test to determine if age distribution and location are independent at the 0.05 level of significance. (a) What is the level of significance? State the null and alternate hypotheses. OH Age distribution and location are not independent. H: Age distribution and location are independent. O Hgi Age distribution and location are not independent. H,: Age distribution and location are not independent. OH Age distribution and location are independent. H: Age distribution and location are independent. O H: Age distribution and location are independent. H: Age distribution and location are not independent.

Yearling 12 31 33 10 34 11 Adult 27 Column Total 92 166 55 51 60 A USE SALT Use a chi-square test to determine if age distribution and location are independent at the 0.05 level of significance. (a) What is the level of significance? State the null and alternate hypotheses. OH Age distribution and location are not independent. H: Age distribution and location are independent. O Hgi Age distribution and location are not independent. H,: Age distribution and location are not independent. OH Age distribution and location are independent. H: Age distribution and location are independent. O H: Age distribution and location are independent. H: Age distribution and location are not independent.

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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**Educational Website Explanation** ### Table: Age Distribution and Location of Buffalo This table presents the age distribution and location of a random sample of 166 buffalo in a national park. #### Data Breakdown: - **Age Categories**: Calf, Yearling, Adult - **Locations**: - Lamar District - Nez Perce District - Firehole District | Age | Lamar District | Nez Perce District | Firehole District | Row Total | |----------|----------------|--------------------|-------------------|-----------| | Calf | 12 | 13 | 16 | 41 | | Yearling | 12 | 11 | 10 | 33 | | Adult | 31 | 27 | 34 | 92 | | Column Total | 55 | 51 | 60 | 166 | ### Chi-Square Test for Independence 1. **What is the level of significance?** - The level of significance is 0.05. 2. **Null and Alternative Hypotheses:** - \( H_0 \): Age distribution and location are independent. - \( H_a \): Age distribution and location are not independent. 3. **Chi-Square Statistic Calculation:** - Determine the expected frequencies for each category combination. - Calculate the chi-square statistic by comparing observed frequencies to expected frequencies. 4. **Expected Frequency Check:** - Are all the expected frequencies greater than 5? - Options: Yes, No 5. **Sampling Distribution and Degrees of Freedom:** - Sampling distribution: Chi-square - Degrees of freedom are calculated as: (Number of rows - 1) * (Number of columns - 1) 6. **P-value Estimation:** - Estimates based on ranges, e.g., \( 0.010 < \text{P-value} < 0.050 \), etc. 7. **Hypothesis Testing Decision:** - Depending on the p-value, determine whether to reject or fail to reject \( H_0 \). 8. **Conclusion Interpretation:** - At the 5% level of significance, a conclusion is drawn about the independence of age distribution and location based on whether \( H_0 \) is rejected or not. By analyzing this data using a chi-square test, researchers can
Transcribed Image Text:**Educational Website Explanation** ### Table: Age Distribution and Location of Buffalo This table presents the age distribution and location of a random sample of 166 buffalo in a national park. #### Data Breakdown: - **Age Categories**: Calf, Yearling, Adult - **Locations**: - Lamar District - Nez Perce District - Firehole District | Age | Lamar District | Nez Perce District | Firehole District | Row Total | |----------|----------------|--------------------|-------------------|-----------| | Calf | 12 | 13 | 16 | 41 | | Yearling | 12 | 11 | 10 | 33 | | Adult | 31 | 27 | 34 | 92 | | Column Total | 55 | 51 | 60 | 166 | ### Chi-Square Test for Independence 1. **What is the level of significance?** - The level of significance is 0.05. 2. **Null and Alternative Hypotheses:** - \( H_0 \): Age distribution and location are independent. - \( H_a \): Age distribution and location are not independent. 3. **Chi-Square Statistic Calculation:** - Determine the expected frequencies for each category combination. - Calculate the chi-square statistic by comparing observed frequencies to expected frequencies. 4. **Expected Frequency Check:** - Are all the expected frequencies greater than 5? - Options: Yes, No 5. **Sampling Distribution and Degrees of Freedom:** - Sampling distribution: Chi-square - Degrees of freedom are calculated as: (Number of rows - 1) * (Number of columns - 1) 6. **P-value Estimation:** - Estimates based on ranges, e.g., \( 0.010 < \text{P-value} < 0.050 \), etc. 7. **Hypothesis Testing Decision:** - Depending on the p-value, determine whether to reject or fail to reject \( H_0 \). 8. **Conclusion Interpretation:** - At the 5% level of significance, a conclusion is drawn about the independence of age distribution and location based on whether \( H_0 \) is rejected or not. By analyzing this data using a chi-square test, researchers can
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