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What is the minimal ssample size needed for a 95% confidence intenval to have a maimal margin of emror of aaz (2) fa prelimirary estimate for pis 024 minimum sample size [ (2) if there is no preliminary estimate for p? minimum sample size

What is the minimal ssample size needed for a 95% confidence intenval to have a maimal margin of emror of aaz (2) fa prelimirary estimate for pis 024 minimum sample size [ (2) if there is no preliminary estimate for p? minimum sample size

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 Content: Determining Minimum Sample Size for Confidence Intervals** --- **Question:** What is the minimal sample size needed for a 95% confidence interval to have a maximal margin of error of 0.02? (a) If a preliminary estimate for \( p \) is 0.24? - **Minimum Sample Size: [_______]** (b) If there is no preliminary estimate for \( p \)? - **Minimum Sample Size: [_______]** --- **Explanation:** This question addresses calculating the minimum sample size required to achieve a specified margin of error for a confidence interval, an important concept in statistics. The sample size ensures that the estimates are reliable and precise. - **Given:** - Confidence Level: 95% - Margin of Error: 0.02 - **Conditions:** - With a preliminary estimate of \( p \): Utilizes the known estimate to tailor the sample size. - Without a preliminary estimate of \( p \): Assumes the maximum variability scenario to ensure coverage. Understanding how to determine the sample size helps in designing studies that yield valid and actionable conclusions. **Note:** Populate the answer fields with calculations or insights into determining sample sizes for these scenarios.
Transcribed Image Text:**Educational Content: Determining Minimum Sample Size for Confidence Intervals** --- **Question:** What is the minimal sample size needed for a 95% confidence interval to have a maximal margin of error of 0.02? (a) If a preliminary estimate for \( p \) is 0.24? - **Minimum Sample Size: [_______]** (b) If there is no preliminary estimate for \( p \)? - **Minimum Sample Size: [_______]** --- **Explanation:** This question addresses calculating the minimum sample size required to achieve a specified margin of error for a confidence interval, an important concept in statistics. The sample size ensures that the estimates are reliable and precise. - **Given:** - Confidence Level: 95% - Margin of Error: 0.02 - **Conditions:** - With a preliminary estimate of \( p \): Utilizes the known estimate to tailor the sample size. - Without a preliminary estimate of \( p \): Assumes the maximum variability scenario to ensure coverage. Understanding how to determine the sample size helps in designing studies that yield valid and actionable conclusions. **Note:** Populate the answer fields with calculations or insights into determining sample sizes for these scenarios.
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