Which of the following statements are correct regarding conf

Which of the following statements are correct regarding confidence intervals and sample size?

Confidence level has no impact on the size of Confidence Intervals.

Greater confidence requires narrower Confidence Interval.

Greater confidence requires wider Confidence Interval.

Smaller sample size gives narrower Confidence Interval.

Solution

the correct alternative is - GREATER CONFIDENCE REQUIRES WIDER CONFIDENCE INTERVAL.

because let (T1,T2) be the confidence interval for paramater p at confidence say 95%

it means that the probability that the interval (T1,T2) would contain p is 0.95

so naturally if we need to increase 0.95 to some extent then the gap between T1 and T2 should also be increased. hence we would get a wider confidence interval.