Question:medium
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
Show Solution
The Correct Option is D
Solution and Explanation
The whole question hinges on the formula for a confidence interval, which is the mean plus or minus a critical value times the standard error. For 95% confidence the critical value from the normal curve is 1.96, conventionally read as 2, so the band runs roughly two standard errors on each side of the mean. That makes the fourth option correct. The first option is backwards, because demanding a higher level of confidence forces a wider band, so lowering the confidence level narrows the interval. The second option is also backwards, since tighter, less scattered data carry a smaller standard error and thus a narrower interval. The third option ignores $SE=SD/\sqrt{n}$, which shows that growing the sample size pulls the standard error down and tightens the interval. Only the statement about 95% covering two standard errors survives. $$\boxed{\text{95\% CI covers about 2 standard errors around the mean}}$$
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