A sample of n = 25 diners at a local restaurant had a mean lunch bill of $16 with a standard deviation of o = $4. We obtain a 95% confidence interval as (14.43, 17.57). Which action will not reduce the margin of error? O sampling from a population with less variability O decreasing the sample size decreasing the confidence level increasing the number of digits for calculating the interval

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**Question: Improve Understanding of Confidence Intervals and Margin of Error**

A sample of \( n = 25 \) diners at a local restaurant had a mean lunch bill of $16 with a standard deviation of \( \sigma = \$4 \). We obtain a 95% confidence interval as (14.43, 17.57). Which action will not reduce the margin of error?

- ○ Sampling from a population with less variability
- ○ Decreasing the sample size
- ○ Decreasing the confidence level
- ○ Increasing the number of digits for calculating the interval

**Explanation for Options:**

1. **Sampling from a population with less variability:** This typically reduces the margin of error since less variability means more reliable estimates.

2. **Decreasing the sample size:** Generally, this increases the margin of error because smaller samples tend to provide less precise estimates, so this is the correct answer.

3. **Decreasing the confidence level:** This usually reduces the margin of error as a lower confidence level means a narrower interval.

4. **Increasing the number of digits for calculating the interval:** This doesn't affect the actual statistical margin of error; it merely changes the precision of how the results are reported.

**Tip:** When assessing actions in statistical analysis, consider how each factor influences the overall precision and reliability of your estimates.
Transcribed Image Text:**Question: Improve Understanding of Confidence Intervals and Margin of Error** A sample of \( n = 25 \) diners at a local restaurant had a mean lunch bill of $16 with a standard deviation of \( \sigma = \$4 \). We obtain a 95% confidence interval as (14.43, 17.57). Which action will not reduce the margin of error? - ○ Sampling from a population with less variability - ○ Decreasing the sample size - ○ Decreasing the confidence level - ○ Increasing the number of digits for calculating the interval **Explanation for Options:** 1. **Sampling from a population with less variability:** This typically reduces the margin of error since less variability means more reliable estimates. 2. **Decreasing the sample size:** Generally, this increases the margin of error because smaller samples tend to provide less precise estimates, so this is the correct answer. 3. **Decreasing the confidence level:** This usually reduces the margin of error as a lower confidence level means a narrower interval. 4. **Increasing the number of digits for calculating the interval:** This doesn't affect the actual statistical margin of error; it merely changes the precision of how the results are reported. **Tip:** When assessing actions in statistical analysis, consider how each factor influences the overall precision and reliability of your estimates.
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