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By how many times does the sample size have to be increased to decrease the margin of error by a factor of 6 The sample size must be increased by a factor of to decrease the margin of error by a factor of (Type a whole number.) What is the general relationship, if any, between the sample size and the margin of error? O A. Increasing the sample size by a factor M results in the margin of error decreasing by a factor of M В. Increasing the sample size by a factor M results in the margin of error decreasing by a factor of M 1 Increasing the sample size by a factor M results in the margin of error decreasing by a factor of M2 O D. There is no relationship between the sample size and the margin of error.

By how many times does the sample size have to be increased to decrease the margin of error by a factor of 6 The sample size must be increased by a factor of to decrease the margin of error by a factor of (Type a whole number.) What is the general relationship, if any, between the sample size and the margin of error? O A. Increasing the sample size by a factor M results in the margin of error decreasing by a factor of M В. Increasing the sample size by a factor M results in the margin of error decreasing by a factor of M 1 Increasing the sample size by a factor M results in the margin of error decreasing by a factor of M2 O D. There is no relationship between the sample size and the margin of error.

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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**Question:** By how many times does the sample size have to be increased to decrease the margin of error by a factor of \( \frac{1}{6} \)? --- **Solution:** The sample size must be increased by a factor of \(\underline{\quad}\) to decrease the margin of error by a factor of \( \frac{1}{6} \). (Type a whole number.) **What is the general relationship, if any, between the sample size and the margin of error?** - **Option A:** Increasing the sample size by a factor \( M \) results in the margin of error decreasing by a factor of \( \frac{1}{M} \). - **Option B:** Increasing the sample size by a factor \( M \) results in the margin of error decreasing by a factor of \( \frac{1}{\sqrt{M}} \). - **Option C:** Increasing the sample size by a factor \( M \) results in the margin of error decreasing by a factor of \( \frac{1}{M^2} \). - **Option D:** There is no relationship between the sample size and the margin of error. --- **Explanation:** Typically, the margin of error (ME) is inversely proportional to the square root of the sample size (n), which means \( ME \propto \frac{1}{\sqrt{n}} \). Thus: - To decrease the margin of error by a factor of \( \frac{1}{6} \), the sample size must be increased by a factor of \( 6^2 = 36 \). The correct answer would be based on this understanding, which aligns with **Option B** as the most parsimonious reasoning.
Transcribed Image Text:**Question:** By how many times does the sample size have to be increased to decrease the margin of error by a factor of \( \frac{1}{6} \)? --- **Solution:** The sample size must be increased by a factor of \(\underline{\quad}\) to decrease the margin of error by a factor of \( \frac{1}{6} \). (Type a whole number.) **What is the general relationship, if any, between the sample size and the margin of error?** - **Option A:** Increasing the sample size by a factor \( M \) results in the margin of error decreasing by a factor of \( \frac{1}{M} \). - **Option B:** Increasing the sample size by a factor \( M \) results in the margin of error decreasing by a factor of \( \frac{1}{\sqrt{M}} \). - **Option C:** Increasing the sample size by a factor \( M \) results in the margin of error decreasing by a factor of \( \frac{1}{M^2} \). - **Option D:** There is no relationship between the sample size and the margin of error. --- **Explanation:** Typically, the margin of error (ME) is inversely proportional to the square root of the sample size (n), which means \( ME \propto \frac{1}{\sqrt{n}} \). Thus: - To decrease the margin of error by a factor of \( \frac{1}{6} \), the sample size must be increased by a factor of \( 6^2 = 36 \). The correct answer would be based on this understanding, which aligns with **Option B** as the most parsimonious reasoning.
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