Which are the three factors that affect the width of a confidence interval?

Which are the three factors that affect the width of a confidence interval?

• A. Sample size, confidence level, and the variability in the data
• B. Confidence level, sample size, and the variability in the data
• C. Variability in the data only
• D. Confidence level only

Answer: (B)

The width of a confidence interval reflects how precise our estimate is, and three things drive it: the confidence level, the sample size, and the variability in the data. If you want more confidence (a higher confidence level), the interval must be wider because you’re using a larger critical value (z* or t*). If you collect more data (a larger sample size), the standard error shrinks, so the interval becomes narrower. If the data are more variable, the standard deviation is larger, which also widens the interval. Since all three factors influence the interval’s width, the option that lists confidence level, sample size, and data variability captures the full set of influences. The other choices omit one or more of these factors, making them incomplete.

The width of a confidence interval reflects how precise our estimate is, and three things drive it: the confidence level, the sample size, and the variability in the data. If you want more confidence (a higher confidence level), the interval must be wider because you’re using a larger critical value (z* or t*). If you collect more data (a larger sample size), the standard error shrinks, so the interval becomes narrower. If the data are more variable, the standard deviation is larger, which also widens the interval. Since all three factors influence the interval’s width, the option that lists confidence level, sample size, and data variability captures the full set of influences. The other choices omit one or more of these factors, making them incomplete.