Confidence Interval- which is narrower? 95%? 99%?

#1
One of my homework question requires me to explain why 99% is narrower 95% but I think its other way around. Am I wrong or the question is a typo?
 

Dragan

Super Moderator
#2
One of my homework question requires me to explain why 99% is narrower 95% but I think its other way around. Am I wrong or the question is a typo?

Yes, a 99% C.I will be wider than a 95% C.I.

Just think of it in terms of a critical value from some probability distribution e.g. standard normal.

For example we could have XBar = 100 with a standard error of 10. Thus, the 95% C.I. would be

100 + - 1.96* 10.

The 99% C.I. would be

100 + - 2.58*10

obviously making it wider than the 95% C.I.
 
#3
I remember this aha moment myself in my first statistics class. Think of the confidence interval as picking things. You are in effect picking things inside the interval as somehow different than things outside the interval.


Now consider a multiple choice question with 5 answers only one right and some how you were allowed to pick all the options. How confident would you be one of the answers you picked would be the right answer? 100% confident because you picked everything!

But now say someone says you can only pick 4. You must be less confident right? And 3 and 2 and 1? Each time you pick less answers no matter how sure you are you know the actual answers you are picking a smaller subset so your confidence that one of the things you picked covers the right answer has to be going down.

In statistics the only 100% confidence interval has every number in it. A single point covers the truth with no confidence. And everything else is between those extremes.

Just ask yourself is one of the intervals smaller than the other? Is the smaller interval wholly contained in the larger interval? If so how could you possibly be more confident that the smaller interval covered the actual answer when the larger interval has the entire smaller interval plus some more "stuff".