Confidence levels? Confusion!

Hey,

As explained in other lectures:

95% confidence gives lesser confidence, however, a narrower interval. 
99% confidence gives higher confidence, however, a wider interval.

Let me give an example:

I don't know your age, Soonita, but I am 95% confident that you are between 18 and 55 years old, based on the fact that you are taking an online Statistics course (which is not much information to begin with. Moreover, I don't have any information about the age of any of our students. As I have no idea about the distribution of student ages, all numbers below are subjectively chosen by me for the purposes of this example).

Now, I am 99% confident that you are between 10 and 70 years old.

I am 100% confident that you are between 0 and 118 years old (the age of the oldest person alive at the time of writing).

Finally, I am 5% confident that you are 25 years old (I chose that completely arbitrarily, obviously).

________

As you can see, there is a trade-off between the level of confidence and the range of the interval. 100% confidence is completely useless, as I must include all ages possible, in order to gain 100% confidence.

99% confidence gives me a much narrower range, but is still not super insightful.

25 years old is a pretty useful estimate -> we have an exact number (in terms of CIs, that would be something along the lines of (25.02 to 25.73)), but the level of confidence of 5% is too small for us to make any sense for any meaningful analysis.

________

95% is the accepted norm, where we don't compromise with accuracy too much, but still get a (comparatively) narrow interval. It's all about the abovementioned trade-off.

To learn more about confidence interval, click here.

Hope that helps!
Best,
365 Team