Question

What happens to the width of the confidence interval as the confidence level drops?

a) Increases
b) Decreases
c) Does not change
d) None of the above

Answer 1

a) Increases

Step-by-step explanation:

Confidence intervals reflect the range within which the true population parameter is likely to fall. As the confidence level drops, indicating a lower level of certainty or confidence in capturing the true parameter, the width of the confidence interval widens. For instance, a 95% confidence level generates a narrower interval compared to a 90% confidence level for the same sample data.

Lower confidence levels imply a willingness to accept a higher probability of the true parameter lying outside the interval, leading to a broader range of values within the confidence interval. This widening occurs to accommodate the increased margin of error associated with lower confidence levels.

Therefore, decreasing the confidence level results in a larger margin of uncertainty and a wider confidence interval, allowing for a higher probability of the true parameter falling within the range specified by the interval.