To determine which actions will reduce the size of the margin of error when constructing a confidence interval for the mean μ of a Normal population with a known standard deviation σ, let's analyze each option step by step:

1. **Use a lower level of confidence**:
- The margin of error (ME) is given by the formula: $ ME = z^* \frac{\sigma}{\sqrt{n}} $, where $ z^* $ is the critical value corresponding to the desired confidence level, $ \sigma $ is the standard deviation, and $ n $ is the sample size.
- A lower level of confidence corresponds to a smaller $ z^* $ value.
- Therefore, using a lower level of confidence will reduce the margin of error.

2. **Increase the sample size**:
- The margin of error formula includes the term $ \sqrt{n} $ in the denominator.
- Increasing the sample size $ n $ will increase $ \sqrt{n} $, which in turn decreases the margin of error.
- Therefore, increasing the sample size will reduce the margin of error.

3. **Reduce σ**:
- The margin of error is directly proportional to the standard deviation $ \sigma $.
- Reducing $ \sigma $ will directly reduce the margin of error.
- Therefore, reducing $ \sigma $ will reduce the margin of error.

Given the analysis above, all the provided options will reduce the size of the margin of error. Therefore, the correct answer is:

**All answers are correct.**

Question

To determine which actions will reduce the size of the margin of error when constructing a confidence interval for the mean μ of a Normal population with a known standard deviation σ, let's analyze each option step by step:

1. **Use a lower level of confidence**:
   - The margin of error (ME) is given by the formula: $ ME = z^* \frac{\sigma}{\sqrt{n}} $, where $ z^* $ is the critical value corresponding to the desired confidence level, $ \sigma $ is the standard deviation, and $ n $ is the sample size.
   - A lower level of confidence corresponds to a smaller $ z^* $ value.
   - Therefore, using a lower level of confidence will reduce the margin of error.

2. **Increase the sample size**:
   - The margin of error formula includes the term $ \sqrt{n} $ in the denominator.
   - Increasing the sample size $ n $ will increase $ \sqrt{n} $, which in turn decreases the margin of error.
   - Therefore, increasing the sample size will reduce the margin of error.

3. **Reduce σ**:
   - The margin of error is directly proportional to the standard deviation $ \sigma $.
   - Reducing $ \sigma $ will directly reduce the margin of error.
   - Therefore, reducing $ \sigma $ will reduce the margin of error.

Given the analysis above, all the provided options will reduce the size of the margin of error. Therefore, the correct answer is:

**All answers are correct.**

Knowee AI · Accepted Answer

To determine which actions will reduce the size of the margin of error when constructing a confidence interval for the mean μ of a Normal population with a known standard deviation σ, let's analyze each option step by step:

1. **Use a lower level of confidence**:
   - The margin of error (ME) is given by the formula: $ ME = z^* \frac{\sigma}{\sqrt{n}} $, where $ z^* $ is the critical value corresponding to the desired confidence level, $ \sigma $ is the standard deviation, and $ n $ is the sample size.
   - A lower level of confidence corresponds to a smaller $ z^* $ value.
   - Therefore, using a lower level of confidence will reduce the margin of error.

2. **Increase the sample size**:
   - The margin of error formula includes the term $ \sqrt{n} $ in the denominator.
   - Increasing the sample size $ n $ will increase $ \sqrt{n} $, which in turn decreases the margin of error.
   - Therefore, increasing the sample size will reduce the margin of error.

3. **Reduce σ**:
   - The margin of error is directly proportional to the standard deviation $ \sigma $.
   - Reducing $ \sigma $ will directly reduce the margin of error.
   - Therefore, reducing $ \sigma $ will reduce the margin of error.

Given the analysis above, all the provided options will reduce the size of the margin of error. Therefore, the correct answer is:

**All answers are correct.**

You plan to construct a confidence interval for the mean μ of a Normal population with (known) standard deviation σ. Which of the following will reduce the size of the margin of error?Use a lower level of confidence.Increase the sample size.Reduce σ.All answers are correct.

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