Question

Explain why confidence intervals are wider (i.e. the difference between the two numbers in the confidence interval is larger) with larger confidence levels (say, 95% rather than 90%) and then explain why it is that way with a smaller sample size.

Answer 1

as we know

Confidence interval is given as:

so, here we can see that for a larger confidence lavel (95%) the critical value is larger (1.96) as compare to the lower confidence interval(90%) i,e value is 1.64.

as critical value is larger, the Margin of Error will be larger, and if margin of error will be larger, the confidence interval band will be wider.

Second part:

here in the margin of error: we can see if Critical value and standard value is constant, if n(sample size) is smaller the value of Margin of error(ME) will be larger, and if margin of error(ME) is larger, Confidence Interval will be wider.