Which of the following results in a wider confidence interval? Assume the sample proportion stays the same.

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BlackTom AI · Accepted Answer

Question restatement: Which of the following results in a wider confidence interval? Assume the sample proportion stays the same.
Options:
1) When a higher confidence level is used.
2) When margin of error is decreased.
3) When using a larger sample.
4) When standard error is decreased.

Analysis of each option:
Option 1: When a higher confidence level is used. This is the correct way a confidence interval becomes wider. Increasing the confidence level (for example from 95% to 99%) requires using a larger critical value (z* or t*) in the margin of error calculation, which expands the interval around the estimate.
Option 2: When margin of error is decreased. A smaller margin of error directly yields a narrower interval, so this does not produce a wider CI.
Option 3: When using a larger sample. A larger sample typically reduces sampling variability and lowers the standard error, which makes the confidence interval narrower, not wider.
Option 4: When standard error is decreased. A smaller standard error reduces the width of the interval, since the margin of error is proportional to the standard error; hence this would not widen the CI.

In summary, only increasing the confidence level widens the interval, while the other options all contribute to narrowing or not affecting the width in the same way.

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Which of the following results in a wider confidence interval? Assume the sample proportion stays the same.

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