Basic statistics question

[Chris Shearer Cooper]

I know this is an easy question, and I was supposed to have learned it
in my statistics class, but that was more years ago than I care to
reveal (grin) ...

There is a random process going on - so every time process X occurs,
there is a Y% chance that it will have outcome Z. Only God knows what
the value for 'Y' is.

I do a random sampling of N times and see how many times outcome Z
occurs.

What can I say now about Y? I assume there's kind of a bell curve,
for example if I sample 10 times and get outcome Z twice, it's very
unlikely (but not impossible) that Y is either 0.01% or 99.99%, but a
high likelihood that Y is somewhere around 20%.

Is there a statistical method (t? student?) that lets me say (for
example) that there is a 66% chance (one std. dev.) that the actual
value for Y is between 15% and 25%?

Thanks,
Chris

[Ray Koopman]

On Aug 10, 9:20 am, Chris Shearer Cooper

You want a confidence interval for a binomial proportion.
There's lots of information about them on the internet. Start with
http://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval

[Chris Shearer Cooper]

Thanks!

Yes, reading the header of that page, that sounds like exactly what
I'm looking for.

So let's say the experiment is rolling a die, where I don't know how
many sides the die has, and I want to know how many times it comes up
'1'. I roll the die 100 times and get a '1' 10 times. My best guess
is that I have a 10-sided die, but I can't say with any certainty. I
might only be able to say "the die most likely has between 9 and 11
sides" or something like that.

Looking at the Wikipedia page, I'm assuming that "proportion estimated
from the statistical sample" means the proportion that I actually
measured in my sample measurement, in my example that would be 0.1.

But I have no idea what a "percentile of a standard normal
distribution" is. Wikipedia isn't packaging up that information for
my easy understanding :-)

Thanks,
Chris

[Chris Shearer Cooper]

On Aug 11, 7:43 am, Chris Shearer Cooper

I just realized I may have confused things ...

I am not looking for how many sides the die has, but what are the odds
of rolling a '1'. So instead of looking for "the die has between 9
and 11 sides", I'm looking for "you will probably roll a '1' between
9% and 11% of the time". A subtle difference, but I have no idea if
it effects the calculation or something.

Chris

[Ray Koopman]

On Aug 11, 7:06 am, Chris Shearer Cooper
<chris.shea...@gmail.com> wrote:
> On Aug 11, 7:43 am, Chris Shearer Cooper <chris.shea...@gmail.com> wrote:
>> On Aug 11, 2:39 am, Ray Koopman <koo...@sfu.ca> wrote:

From where you seem to be, the learning curve to get to understanding
confidence limits is pretty steep. You might want to look for an
online intro to statistics such as http://davidmlane.com/hyperstat/

[Chris Shearer Cooper]

On Aug 12, 10:22 pm, Ray Koopman <koop...@sfu.ca> wrote:
> On Aug 11, 7:06 am, Chris Shearer Cooper
>
>
>

> <chris.shearer.coo...@gmail.com> wrote:
> > On Aug 11, 7:43 am, Chris Shearer Cooper <chris.shearer.coo...@gmail.com> wrote:
> >> On Aug 11, 2:39 am, Ray Koopman <koop...@sfu.ca> wrote:

That looks like a good web site, but I'm still pretty overwhelmed, I'm
not even sure where to start.

How hard is it for you to take me through one equation - for example,
my sample where I roll the N-sided die 10 times and roll a '1' exactly
once - and then I will know which parts of the David M. Lane web site
I need to focus on?

Thanks,
Chris

[Ray Koopman]

On Aug 14, 6:17 pm, Chris Shearer Cooper

Using the Wilson interval from the Wikipedia page
n = # of rolls = 10
x = # of '1's = 1
^p = x/n = 1/10
confidence alpha z interval
90% .10 1.64485 (.023, .348)
95% .05 1.95996 (.018, .404)
99% .01 2.57583 (.012, .507)

[Chris Shearer Cooper]

Excellent - thanks!
Chris