5.1.3 Effect of Alpha and Sample Size on Confidence Interval

Introduction

• Overview: Examining how the confidence level (alpha) and sample size affect the width of confidence intervals in statistical analysis.

Confidence Coefficient and Margin of Error

• Impact of Confidence Coefficient:
• Increasing the confidence level from 80% to 99% increases the margin of error, making the confidence interval wider. This reflects higher certainty but reduces precision.
• A 100% confidence level would theoretically require an infinite margin of error, rendering the interval useless.

Optimal Confidence Coefficient

• Application-Specific:
• The choice of confidence level depends on the stakes of being wrong. High-stakes scenarios (like FDA approvals) might require 95% or 99% confidence intervals.
• In less critical contexts, a lower confidence level (e.g., 90%) might be acceptable if the cost of error is low.

Influence of Sample Size

• Sample Size Impact:
• The margin of error decreases inversely with the square root of the sample size. A larger sample size yields a smaller margin of error, enhancing the confidence interval's precision.
• Determining the "optimal" sample size involves balancing the desired precision (small margin of error) against practical constraints like cost and feasibility.

Practical Application

• Decision Making:
• Consistency in choosing a confidence coefficient is crucial when comparing different decision options to ensure comparability.
• The formula for margin of error is commonly used to calculate the necessary sample size to achieve a specific margin of error, balancing accuracy with resource constraints.

Conclusion

• Summary: This module underscores the importance of selecting appropriate confidence levels and sample sizes in statistical inference to optimize decision-making processes based on the data collected.

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