Question

How will the width of a confidence interval change (if at all) in each of the following cases?

A) Sample standard deviation decreases:         a) increase     b) decrease     c) stay the same

B) Sample size decreases:         a) increase      b) decrease      c) stay the same

C) You change from a 95% CI to a 99% CI:       a) increase      b) decrease      c) stay the same

Answer 1

Confidence interval increases (or decreases), as margin of error or equivalently the standard error increases (decreases) .  

Now standrd error is defined as :   

and margin of error :

So, a) If sample sd decreases , the standard error decreases too , resulting in decrease of width of CI .

b) If sample size decreases , the standard error imncreases , resulting in increase of width of CI.

c) As we increase the level of confidence , the absolute value  critical value also increases , thus resulting in increase of the width of CI .

Think of it as this : You have some information , you calculate a CIwith 95% confidence level .Now you have the same amount of info , but you want to be more sure , so definitely you would need a wider CI .