Question:
Which of the following statements about confidence limits or interval is true?
Which of the following statements about confidence limits or interval is true?
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Recall that 95% confidence equals mean plus or minus 1.96 standard errors.
Updated On: Jun 24, 2026
- Smaller the confidence level, larger will be the confidence interval
- Less variable the data, wider will be the confidence interval
- Sample size does not affect the confidence interval
- 95% confidence interval will cover 2 standard errors around the mean
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The Correct Option is D
Solution and Explanation
Step 1: A confidence interval is the mean plus or minus a multiple of the standard error. For a 95% confidence interval the multiple is about 1.96, which is rounded to 2. So the 95% CI is roughly the mean plus or minus 2 standard errors. This makes option D true.
Step 2: A higher confidence level needs a wider interval, so a smaller confidence level gives a narrower interval, not a larger one. Option A reverses this and is false.
Step 3: Less variable data have a smaller standard deviation and therefore a smaller standard error, which gives a narrower interval, not a wider one. So option B is false.
Step 4: A larger sample size shrinks the standard error because \(SE = \frac{SD}{\sqrt{n}}\), so sample size strongly affects the width of the interval. Option C is false.
The correct answer is option D.
Step 2: A higher confidence level needs a wider interval, so a smaller confidence level gives a narrower interval, not a larger one. Option A reverses this and is false.
Step 3: Less variable data have a smaller standard deviation and therefore a smaller standard error, which gives a narrower interval, not a wider one. So option B is false.
Step 4: A larger sample size shrinks the standard error because \(SE = \frac{SD}{\sqrt{n}}\), so sample size strongly affects the width of the interval. Option C is false.
The correct answer is option D.
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