## What We Mean By x

[ Oh, wow. Yesterday’s entry had way fewer hits than average. I also put an equation out right up front where everyone could see it. I wonder if this might be a test of Stephen Hawking’s dictum about equations and sales. Or maybe I was just boring yesterday. I’d ask, but apparently, nobody found me interesting enough yesterday to know for comparison. ]

It shouldn’t be too hard to translate the the idea “I want to know the population of Charlotte at some particular time” into a polynomial. The polynomial ought to look something like y equals some pile of numbers times x’s raised to powers, and x somehow has to do with the particular time, and y has something to do with the population. And it’s not hard to do that translating, but I want to talk about some deeper issues. It’s probably better explaining them on the simple problem, where we know what we want things to mean, than it would be explaining them for a complicated problem.

## A Polynomial Of What?

[ According to the WordPress statistics, trapezoids are just the hook bringing people into here. I didn’t realize there was such a big community of people who need trapezoid information. If I did I’d have played up my search engine terms more. ]

If anyone had doubts about using polynomials as a generally good thing I hope either the doubts or the doubters are quieted now. My next couple goals are simple ones: I want to set up polynomials to interpolate what the population of Charlotte, North Carolina, was around 1975. That is, I’ll be creating at least one equation of the form $y = a_0 + a_1 \cdot x + a_2 \cdot x^2 + a_3 \cdot x^3 + \cdots + a_n \cdot x^n$ where somehow the right choices of numbers for $a_0, a_1, a_2$, et cetera will mean if I put the right number in for x I’ll get out of it an estimate of the population. I’ve got symbols. I need to figure what I want them to mean.

## Finding, and Starting to Understand, the Answer

If the probability of having one or fewer clean sweep episodes of The Price Is Right out of 6,000 aired shows is a little over one and a half percent — and it is — and we consider outcomes whose probability is less than five percent to be so unlikely that we can rule them out as happening by chance — and, last time, we did — then there are improbably few episodes where all six contestants came from the same seat in Contestants Row, and we can usefully start looking for possible explanations as to why there are so few clean sweeps. At least, that’s the conclusion at our significance level, that five percent.

But there’s no law dictating that we pick that five percent significance level. If we picked a one percent significance level, which is still common enough and not too stringent, then we would say this might be fewer clean sweeps than we expected, but it isn’t so drastically few as to raise our eyebrows yet. And we would be correct to do so. Depending on the significance level, what we saw is either so few clean sweeps as to be suspicious, or it’s not. This is why it’s better form to choose the significance level before we know the outcome; it feels like drawing the bullseye after shooting the arrow the other way around.