Fun with Confidence Intervals – Part 1

If I said the words “confidence intervals” would you know what I meant? What if I also asked if you could calculate them?

If you answered no to either one of these questions I assure you will be able to answer yes by end of this two part series. Oh, and my famous money back guarantee is in play here too.

Population versus Sample Parameters

When we speak about statistics there are two types of parameters in play – population and sample.

We are dealing with the population parameters (mu and sigma) when we are able to collect all the data that ever was and ever will be.

For example, upon last check, I see there are 302,730,073 “legal” citizens living in the USA. If we also assume all of these people are registered to vote (yeah I know babies can’t vote but just work with me here) and they all actually turn out to vote for their favorite candidate we are dealing with population statistics since the entire country came out to vote.

However, since many American’s, for a reason beyond my comprehension, don’t take the time to register and then actually vote we normally have a much smaller SAMPLE of people choose who the next President of the USA will be. So, in this case, we are dealing with sample parameters (Xbar and s).

This is an important discussion if we are to understand confidence intervals so please re-read this section if you didn’t quite grasp it. It’s OK, I’ll wait. Go on and re-read it.

What are Confidence Intervals?

OK, now that we understand the difference between population and sample parameters let’s press on.

As you might imagine we rarely deal with population statistics. In a factory, for example, it is highly unlikely you are able to measure each part produced. Instead, you will likely pull samples out from time to time in order to gauge how well the process is performing.

When we sample like this we are actually attempting to estimate the “true” population parameters (mu and sigma) with sample parameters (Xbar and s). And since there is variation in every process these estimates will always have a certain amount of uncertainty associated with them.

The question we must next ask is how much uncertainty are we talking about? Ahhh… this my good friends is where confidence intervals come into play!

Come back tomorrow night and I will show you how to actually do this.

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3 Comments

  1. William Phillips

    August 29, 2007 - 9:04 pm

    I really appreciate the time you take for these posts and how you make topics I have struggled to understand easy to grasp. Keep up the great work!

  2. Ron Pereira

    August 30, 2007 - 7:16 am

    Thank you for the kind words William. I remember being so frustrated with teachers and professors who seemed to take joy in confusing their students.

    I do my best to take the opposite approach on this blog and in my day job.