Notes for 9/5/12

Here is a link to the topics for this Wednesday, September 5.

We will also discuss ordered and unordered categorical data and the problems with Excel using some of these ideas.

Early definitions.

A link to a post about definitions.  The post has more information than we went over in class.  We will get to this stuff all this stuff in the next few classes on Friday and Monday.

These notes are taken from a class taught in two hour sessions, so there will often be extra info.  You can read it to stay ahead.

Hans Rosling 200 countries, 200 years, 4 minutes

Here is Hans Rosling's 200 countries and 200 years in four minutes. Here are some questions from the four minutes.

What does the x axis represent?
Are the x axis numbers linearly larger? (This question was addressed in class.)
What does the y axis represent?
Are the y axis numbers linearly larger? (This question was addressed in class.)
What does the color of a dot represent?
What does the size of a dot represent?
Which continent has the most countries getting healthier and wealthier in the 19th Century, due in large part to the Industrial Revolution?
Rosling stops for a pair of global catastrophes that overlapped in time. What are they?
At the end of World War II, what country is in the lead in terms of health and wealth?
In 2009, what country is in the lead in terms of health and wealth?
In 2009, what country is far behind in terms of health and wealth?
When splitting up China, Shanghai is about on par with ______ while rural parts of Guizhou are on par with _____.

Watch the video and answer the questions. The video doesn't fit the screen very well, so click on it and watch it on YouTube.
(Answers in the comments.)

Stuff to review for the second midterm.

The second midterm will cover topics from Homeworks 6, 7, 8, 9 and 10. These will include:

Distributions from independent trials (sampling with replacement)
Distributions from dependent trials (sampling without replacement)
Margins of error from opinion poll percentages (also know as the 95% confidence interval)
The confidence of victory formula
Sentences that explain margin of error and confidence of victory numbers
Modern and classic pari-mutuel payoffs (profit and risk)
Expected Value of a win-lose game
Hypothesis testing
Rejecting the null hypothesis and failing to reject the null hypothesis
Type I error (rejecting the null when you shouldn't)
Type II error (failing to reject the null when you should)
Formulas for creating the test statistic for hypothesis testing (z-scores and t-scores)
Finding the threshold number for hypothesis testing (one-tailed high, one-tailed low, two tailed)

More on hypothesis testing

True false questions about hypothesis testing.
The basic facts about hypothesis testing.


Practice problems

In testing for psychic powers, researchers use a deck with five different shapes, as shown in the picture on the left. If the deck is re-shuffled every time, the probability of guessing correctly by pure chance is 1/5 or p = .2 written in decimal. The test would be one tailed high, and we use the z-score table, so the threshold for 95% confidence is = 1.645 and the threshold for 99% confidence is z = 2.325.

Questions:

1. If a subject gets 3 out of 10 correct in a psychic test, are we 95% confident the subject shows psychic powers?

2. If a subject gets 4 out of 10 correct in a psychic test, are we 95% confident the subject shows psychic powers? Are we 99% confident?

3. If a subject gets 5 out of 10 correct in a psychic test, are we 95% confident the subject shows psychic powers? Are we 99% confident?

4. If a subject gets 30 out of 100 correct in a psychic test, are we 95% confident the subject shows psychic powers? Are we 99% confident?

5. If n = 100 and p = .2 in a high one tailed test, find the minimum number of correct answers for rejecting H0 to the 95% confidence level and the 90% confidence level.

Answers in the first comment.

Bonus questions

We have a sample with n = 40, x-bar = 172.5 and sx = 119.5.

1. What is the one tailed low threshold for 95% confidence?

2. What is the one tailed high threshold for 99% confidence?

3. If H0 is mux = 200, are we 95% confident we can reject this for HA: mux < 200?

4. If H0 is mux = 100, are we 99% confident we can reject this for HA: mux > 100?

Answers in second comment.

Practice problems for confidence of victory and confidence intervals

Links to earlier posts about confidence of victory.

Data from recent polls.

Boxer vs. Fiorina U.S. Senate (CA)
Date: 10/2
Boxer: 49%
Fiorina: 44%
n = 448

Brown vs. Whitman Governor (CA)
Brown: 50%
Whitman: 43%
n = 448

For both of these polls:
1) Find the 95% confidence interval for both candidates
2) Since the two top candidate poll over 90% total, do the confidence of victory, rounding to the nearest 5% if the value is under 90% and to the nearest 1% if the value of over 90%.

Answers in the comments.

Practice problems for homework 5

Contingency problem practice.

Bayesian contingency practice.

Frequency and relative frequency.

Using RANDI(1,10) on the TI-30XIIs a number of times, I get these frequencies. Find n and the relative frequencies, written as exact decimals.

f(1) = 7
f(2) = 7
f(3) = 6
f(4) = 6
f(5) = 3
f(6) = 2
f(7) = 5
f(8) = 5
f(9) = 6
f(10) = 3

Answers to last part in comments.