Day 13: STA205 - Introduction to Statistical Methods

Last time Next time

Announcements:
- Your first exam is coming up next time, this Thursday -- it will cover through Packet 5: the complete story of $p$!
  - Bring a calculator.
  - You will receive a formula sheet (which you can view on-line here)
  - You will receive a Z-table.
  - You will also receive scratch paper, if you need it.
- We'll review today.
- Your quiz is returned:
  - Hypotheses will generally be written with colons (:), and, in this case, with a mention of the population parameter $p$!
    You're sort of missing the main point if you don't mention the parameter.
    $H_o:\ p=.286$ and $H_a:\ p<.286$.
  - Because the ACS has spent a lot of time and money evidently ("after significant advertising campaigns"), we'd better be able to see a decrease. So let's set a high bar with a low $\alpha$ (perhaps $\alpha=.01$).
    Critical: $\alpha$ is chosen before the sample is taken. Otherwise, you would be tempted to set the level of significance to get the answer you want....
  - Two parts (and one important note): we don't usually know that we've committed the error. So some of you were worried that the ACS will be sued, will have their reputation sullied, etc. If they knew that they'd made the error, then they could unmake it! That's the real problem with these errors -- they're silent!
    - Type I
    - The ACS will believe that their campaign has succeeded, when it in fact didn't. They might ramp it up, and make it nationwide, and waste a boatload of money for little or no impact.
    - The citizens of KY will believe that their smoking rates are down, when they're not. They may continue to see advertising that is ineffective.
- Evidence of Man-Made Global Warming Hits 'Gold Standard'
  Confidence that human activities have been raising the global temperature at Earth's surface is at a "five-sigma" level, a statistical gauge meaning there is only a one-in-a-million chance that the signal would appear if there was no warming, Reuters reports.
Let's start by wrapping up the last page of Packet 5:
1. discover the sample size needed to estimate $p$ with given confidence.
Then we'll turn to reviewing.

Links:

The Standard Normal Table of probabilities.
Statcrunch instructions:
- Load the Stop and Frisk Data for packet 2. Load it by "WWW address", and make sure to set the delimiter to "comma" (because this is a "csv" (comma-separated values) file.
- Once the data is loaded, click on "Graph" or "Table".
- Alternatively, you may want to join my "group" on Statcrunch. That way you can access the data more quickly. It's Sta205-Long, if you want to add yourself into that group.
- For the IMath homework, you'll need the Bipolar Depression Study data. Same thing: Load it by "WWW address", and make sure to set the delimiter to "comma" (because this is a "csv" (comma-separated values) file (or get it from the group).

Today, if we have a little more time, we will startPacket 5), which has two major objectives:

estimate parameter $p$ using statistic $\hat{p}$, with given confidence, and
discover the sample size needed to estimate $p$ with given confidence.

Let's remind ourselves about the distribution of $\hat{p}$:

Now in this case we don't have $p$. We want to find $p$. So how do we proceed? That's the subject of this packet.

Links:

Please watch Brooke's Hypothesis test for the proportion at some point.
The Standard Normal Table of probabilities.
Interview with Richard Feynman

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