What does a narrow confidence interval indicate about the precision of the estimate?

What does a narrow confidence interval indicate about the precision of the estimate?

• A. More precise estimate
• B. Less precise estimate
• C. Higher p-value
• D. Larger sample size required

Answer: (A)

The width of a confidence interval reflects how precisely we’ve pinned down the parameter. A narrow interval means the true value is believed to lie in a tight range around the estimate, indicating greater precision. This comes from a smaller margin of error, which happens when there’s less variability in the data or a larger amount of information (larger sample size) used to compute the estimate, all while keeping the same confidence level. The p-value is about whether the observed effect is likely under the null hypothesis, not how precisely we’ve estimated the parameter. The width of the interval is not a direct statement about needing a larger sample; it reflects the current precision of the estimate given the data and the chosen confidence level. So, a narrow confidence interval signals a more precise estimate.

The width of a confidence interval reflects how precisely we’ve pinned down the parameter. A narrow interval means the true value is believed to lie in a tight range around the estimate, indicating greater precision. This comes from a smaller margin of error, which happens when there’s less variability in the data or a larger amount of information (larger sample size) used to compute the estimate, all while keeping the same confidence level.

The p-value is about whether the observed effect is likely under the null hypothesis, not how precisely we’ve estimated the parameter. The width of the interval is not a direct statement about needing a larger sample; it reflects the current precision of the estimate given the data and the chosen confidence level.

So, a narrow confidence interval signals a more precise estimate.