Questions: A researcher computed a 90% confidence interval for the mean age of college students. If the researcher had instead used a 95% confidence interval, then the computed margin of error would have been smaller.

A researcher computed a 90% confidence interval for the mean age of college students. If the researcher had instead used a 95% confidence interval, then the computed margin of error would have been smaller.

Transcript text: A researcher computed a $90 \%$ confidence interval for the mean age of college students. If the researcher had instead used a $95 \%$ confidence interval, then the computed margin of error would have been smaller.

Solution

Solution Steps

Step 1: Understand the relationship between confidence level and margin of error

The margin of error in a confidence interval is influenced by the confidence level. A higher confidence level (e.g., 95%) requires a larger margin of error compared to a lower confidence level (e.g., 90%) because it aims to capture a wider range of possible values to ensure greater certainty.

Step 2: Analyze the given statement

The statement claims that using a 95% confidence interval instead of a 90% confidence interval would result in a smaller margin of error. This is incorrect because, as established in Step 1, a higher confidence level leads to a larger margin of error, not a smaller one.

Step 3: Conclusion

Based on the relationship between confidence level and margin of error, the statement is False.