Suppose you were to analyze data from a study of 45 herds of wild horses where some of the females in each herd were being treated with contraceptives to keep them from getting pregnant. The wildlife managers in the area want to find out if the contraceptive treatment is working. Suppose in your analysis, you were to find a linear correlation of r = -0.56 between the proportion of females in a herd that had received the contraceptive treatment (the x variable) and the number of foals born in that herd (the y variable). One way to test the statistical significance of a correlation coefficient is to compare it with the appropriate critical value of r in Table A-6. Use this Table A-6 method and an a = 0.05 significance level to determine whether the correlation coefficient you found in the previous puzzle is significantly different from zero. Provide the appropriate critical value ret and a complete, written-out conclusion that explains what the correlation means, including in terms of whether the contraceptive treatment is working or not.

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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**Transcript of Study Analysis:**

**Date:** October 30, 2023, at 11:00 AM

**Topic: Analyzing the Effectiveness of Contraceptive Treatments in Wild Horse Herds**

**Study Overview:**
Imagine conducting an analysis on data from a study involving 45 herds of wild horses. In these herds, some female horses received contraceptive treatments to prevent pregnancies. The aim of wildlife managers is to determine the effectiveness of these treatments.

**Key Analysis:**
In the analysis, a linear correlation of \( r = -0.56 \) was discovered. This correlation relates the proportion of females in a herd that received the contraceptive treatment (x-variable) to the number of foals born in the herd (y-variable).

**Statistical Significance Testing:**
One method to assess the statistical significance of a correlation coefficient is by comparing it to a critical value from Table A-6. For this analysis, utilize the Table A-6 method with a significance level \( \alpha = 0.05 \).

**Objective:**
Evaluate whether the correlation coefficient significantly differs from zero. This involves determining the critical value and presenting a comprehensive conclusion regarding the meaning of the correlation. The conclusion should address the effectiveness of the contraceptive treatment.

**Next Steps:**
- Identify the critical value from Table A-6 for the given significance level.
- Compare the calculated correlation coefficient to this critical value.
- Conclude whether the contraceptive treatment is effective based on the statistical analysis. 

This study aims to provide insights into the management of wild horse populations through the application of contraceptive methods.
Transcribed Image Text:**Transcript of Study Analysis:** **Date:** October 30, 2023, at 11:00 AM **Topic: Analyzing the Effectiveness of Contraceptive Treatments in Wild Horse Herds** **Study Overview:** Imagine conducting an analysis on data from a study involving 45 herds of wild horses. In these herds, some female horses received contraceptive treatments to prevent pregnancies. The aim of wildlife managers is to determine the effectiveness of these treatments. **Key Analysis:** In the analysis, a linear correlation of \( r = -0.56 \) was discovered. This correlation relates the proportion of females in a herd that received the contraceptive treatment (x-variable) to the number of foals born in the herd (y-variable). **Statistical Significance Testing:** One method to assess the statistical significance of a correlation coefficient is by comparing it to a critical value from Table A-6. For this analysis, utilize the Table A-6 method with a significance level \( \alpha = 0.05 \). **Objective:** Evaluate whether the correlation coefficient significantly differs from zero. This involves determining the critical value and presenting a comprehensive conclusion regarding the meaning of the correlation. The conclusion should address the effectiveness of the contraceptive treatment. **Next Steps:** - Identify the critical value from Table A-6 for the given significance level. - Compare the calculated correlation coefficient to this critical value. - Conclude whether the contraceptive treatment is effective based on the statistical analysis. This study aims to provide insights into the management of wild horse populations through the application of contraceptive methods.
Expert Solution
Step 1: Mentioning the given data and stating the objective

The given data is as follows:

Sample size, straight n equals 45

Correlation coefficient, straight r equals negative 0.56

straight alpha equals 0.05

The objective is to compare the value of straight r with appropriate critical value to get to the desired conclusion.

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