Given specific sample data which confidence interval is wide

Given specific sample data, which confidence interval is wider: the 95 % confidence interval or the 80% confidence interval? Why?

Solution

95 % confidence interval is wider, the reason is it is directly proportional to confidence level. The more you increase the confidence width is incresed.

CI = p ± Z a/2 Sqrt(p*(1-p)/n)))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval