# Estimation

• ### Capture-Recapture with Smarties

Students use the capture-recapture method to estimate the size of a population of SmartiesTM candies. The variability in their estimates is also examined.

• ### Capture-Recapture with M&M's

Students use the capture-recapture method to estimate the size of a population of M&M'sTM.

• ### Target Practice

Lyrics © 2015 by Larry Lesser, music by Dominic Dousa

Salary is the variable whose data I tabulate;
Mean is the parameter I want to estimate.

When I calculate its counterpart
From the sample now in hand,
I wonder if on average,
The bullseye's where it lands!

It's unbiased 'cause on average
the estimate will land
Centered at the target
of the population parameter.

• ### Super Bowl Poll

Lyrics & Music © 2015 Lawrence M. Lesser

"Will the Steelers win next season's Super Bowl?"
The margin of error was 3%
That's roughly the reciprocal of the square root of n.

17% answered 'YES' in the poll,
But what could it be for the population as a whole?
At the 95% level of confidence
The interval goes from 14 to 20%.

If we multiply the sample size by a factor of 9,
The new margin of error that we could find
Would be a third as large as what we had before.
Thanks to the formula, you know the score.
Go Steelers!

• ### Height of Confidence

Lyrics © 2015 by Larry Lesser, music by Dominic Dousa

For a population, there is a parameter
We want to learn about it, it's the number that we're after
Our best guess for its value is the sample statistic
The method we use to get it should make us optimistic!

We'll estimate proportions from opinion polls
Or estimate the mean height from our class rolls.
We hope our sample targets the parameter unknown;
We want a likely range stated as a zone.
When we seek that interval, it's always good to know
What would make it shrink and what would make it grow.

The interval gets tighter with increasing n:
The added information helps us narrow in!
The interval gets bigger with a larger s,
That has come from a sample that's a more uncertain mess!
The interval gets wider for higher confidence
'Cause you have to cover lots more of your bets!

Our sample gives us one shot to make a decent guess
So let's use a method with a high rate of success!
I'm eighty percent confident my answers are first rate,
In my estimation, when we estimate!

• ### Estimation Notation, It's Greek (and Roman) to me

Lyrics © 2015 by Larry Lesser, music by Dominic Dousa

Greek letters refer to the population.
Mu (μ) stands for mean, sigma's (σ) standard deviation,
Greek letters refer to the population.
Beta (β) is the slope, rho (ρ) is the correlation.

Description of part, not whole
that's what sample statistics are:
standard deviation's s, the mean is x-bar () ,
the slope is b, the correlation's r.

A sample statistic estimates a population parameter;
Now that we know this, we're sure to be no statistical amateur!