By how many times does the sample size have to be increased to decrease the margin of error by a factor of ..... The sample size must be increased by a factor of 1 to decrease the margin of error by a factor of 5' (Type a whole number.) What is the general relationship, if any, between the sample size and the margin of error? OA. 1 Increasing the sample size by a factor M results in the margin of error decreasing by a factor of M- О в. Increasing the sample size by a factor M results in the margin of error decreasing by a factor of 1 M 1 OC. Increasing the sample size by a factor M results in the margin of error decreasing by a factor of VM O D. There is no relationship between the sample size and the margin of error.

MATLAB: An Introduction with Applications
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**Sample Size and Margin of Error Relationship**

**Question:**
By how many times does the sample size have to be increased to decrease the margin of error by a factor of \( \frac{1}{5} \)?

The sample size must be increased by a factor of [____] to decrease the margin of error by a factor of \( \frac{1}{5} \).  
*(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 \( \frac{1}{M^2} \).
  
- **Option B:** Increasing the sample size by a factor \( M \) results in the margin of error decreasing by a factor of \( \frac{1}{M} \).

- **Option C:** Increasing the sample size by a factor \( M \) results in the margin of error decreasing by a factor of \( \frac{1}{\sqrt{M}} \).

- **Option D:** There is no relationship between the sample size and the margin of error.
Transcribed Image Text:**Sample Size and Margin of Error Relationship** **Question:** By how many times does the sample size have to be increased to decrease the margin of error by a factor of \( \frac{1}{5} \)? The sample size must be increased by a factor of [____] to decrease the margin of error by a factor of \( \frac{1}{5} \). *(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 \( \frac{1}{M^2} \). - **Option B:** Increasing the sample size by a factor \( M \) results in the margin of error decreasing by a factor of \( \frac{1}{M} \). - **Option C:** Increasing the sample size by a factor \( M \) results in the margin of error decreasing by a factor of \( \frac{1}{\sqrt{M}} \). - **Option D:** There is no relationship between the sample size and the margin of error.
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