Worked out Solution to the "arrows problem" from class.

Here is a link to the Arrows problem key from class on Wednesday.

Unit IV - From Randomness to Probability... Part 1

By now you should have some basic probability rules down...

Like maybe P(A or B) = P(A) + P(B), assuming the two events A and B are independent. And also P(A and B) = P(A)*P(B), assuming the two events A and B are disjoint. And you also should be able to tell the difference between disjoint and independent.

And then the rules had to go and get more complicated (or did they). Lets remove those darn conditions and get a general rule that works for events disjoint, independent or not. The General Addition Rule states that P(A or B) = P(A) + P(B) - P(A and B). This works for both disjoint and, well, joint events. If A and B are disjoint then P(A and B) = 0 so you just get the first addition rule listed above, and if they are not disjoint then subtracting P(A and B) subtracts the overlap, in other words the part of A that was counted in P(A) and in P(B) so therefore counted twice so if not subtracted off, its double counted.

There is also The General Multiplication Rule P(A and B) = P(A)*P(B|A). Which if you didn't know that you probably thinking, "yeah that helps thanks I don't even know how to read that." Ok so you read it like this "The probability of both A and B happening is equal to the probability of A, times the probability of B, given A." I had you up to that given part didn't I. We're talking conditional probability here. P(B|A) means the probability of B, knowing that A has happened. Did you click the link on disjoint and independent above (or right there in front of you now)? The example in there is on drawing a card from a deck of 52. Here's another example with cards. If we draw two cards at random from a well shuffled deck, what is the probability that the first one is red, and the second one is also red. The probability of the first one being red is 26/52 or 1/2, if we don't put the first card back then the probability that the second one is red is not 1/2, its 25/51 because we have one red card out of the deck. So P(A) = 1/2 and P(B|A) = 25/51. So P(A and B) = (1/2)*(25/51).

Here's my favorite (and yes it is possible to have a favorite probability rule, you probably have a favorite quadrilateral and your not even a math teacher, admit it you like rhombus the best don't you). The Complement Rule this basically is a rule because something has got to happen. So I've got kids. If I tell you that the probability that my daughter is sleeping right now (at 10:50 pm), is 90% you should be able to give me the probability that she is not sleeping right? 10%. This is basically the complement rule in action. P(sleeping) = .9, then P(not sleeping) = 1 - .9 = .1. For any event it either happens or it doesn't. So something's got to happen, P(A) = 1 - P(~A) the ~A is read "not A" or the "complement of A." This rule is very helpful in "at least" or "at most" problems. For example if I draw three cards at random from a well shuffled deck of cards what is the probability that I draw at least one red? You could calculate the probability of drawing one red, drawing two reds, drawing three reds and then add them up or figure out the probability that you don't get a red, and subtract from 1. Since drawing no reds is the complement of drawing at least one red.

I'd say that's it in a nut shell, but I'm not a mime, and because there's more... but that's another post.

The Placebo Effect

Is the placebo effect is increasing in the U.S.? Check out this article.

There is also something interesting called the Hawthorne Effect.

Excercise for Better Grades

Does Exercising more improve grades?
A recent New York Times article addresses this question.

June 3, 2010, 12:21 pm

Vigorous Exercise Linked With Better Grades

By TARA PARKER-POPE

College students who want to boost their grades can start by boosting their level of exercise, new research suggests.

A report presented on Thursday at the American College of Sports Medicine’s 57th annual meeting in Baltimore finds that college students who regularly engage in vigorous exercise get better grades. Although a link between physical activity and higher academic achievement has been shown in middle-school students, it hasn’t been clear whether exercise is associated with better grades among older students.

To find out, researchers at Saginaw Valley State University in Michigan tracked the grades and exercise habits of 266 undergraduates. They found that students who regularly participated in vigorous physical activity had higher G.P.A.’s.

But does exercise really boost grades — Continue Reading...

Mythbusters lightbulb experiment 2/2

Mythbusters lightbulb experiment 1/2

Sampling Plans - In the news

In a news Article posted by CNN on 10/4/2010 you can get some information on the sampling plan and how you should write up a sampling plan.

"The poll of 1,006 adult Americans, of which 921 were registered voters, was conducted by phone October 27-30, before the midterm elections.

The sample also included 500 respondents who describe themselves as Republicans or independents who lean Republican, and 453 respondents who describe themselves as Democrats or independents who lean Democratic. The survey's overall sampling error is plus or minus 3 percentage points.

CNN also conducted exit polls on Election Day in some of the states that vote first in the presidential primary calendar.

In Iowa, 21 percent of Republicans questioned as they exited the voting booth said that Romney was their likely choice in the 2012 Iowa caucuses, with Huckabee also at 21 percent, Palin at 18 percent, Gingrich at 7 percent and one in five saying they would support another possible candidate.

In New Hampshire, 39 percent of Republicans said that Romney is their likely choice in the state's primary, with Palin at 18 percent, Huckabee at 11 percent, Gingrich at eight percent and 19 percent saying they would back another possible contender.

Twenty-five percent of South Carolina Republicans say Palin would be their likely primary choice, followed by Huckabee at 24 percent, Romney at 21 percent and Gingrich at 10 percent."

For the full article click here.

Notes for Chapter 9

Here are some pretty detailed notes to go along with what we talked about in class regarding Regression Wisdom.

Chapter 9 - Regression Wisdom

There are about 6 subtopics to consider in this chapter. None of this is 100% new, it really helps to prevent you from using regression in the wrong way, and what characteristics of the data could could make the regression equation less valuable than you originally thought.

Here is a website to help you understand cornell notes, that you can then use to help take notes on this chapter.

http://www.cdlilly.com/study_cornell_notes.htm

Extra Review Problems for AP Stats Make Up Day

Here are some review problems. Come on in tomorrow morning for the answers.

FOR FRIDAY 9/25

Just a reminder that this Friday is your retest for chapters 1 - 6. Take time this week to come in and look over your test, get any questions answered, and STUDY!!!

Have a great week :)

Review Homework Key

Here is a link to the key from today's in class review packet.

Review Guide Key

Here is a second video that shows the solution to the ISU problem. What is the percentage of the total group of 2009 test takers modeled by N(21.1, 5.1) does the middle 50% of the 2010 incoming freshman class fall into.

Using the TI - Normalcdf

In class we began working with the TI-83/84 to find percentages under the Normal curve. Check out this document if you forgot how to use the Normalcdf( function on your TI calculator.

"After reviewing the play, the ruling on the field has been overturned." Please mentally substitute the word "interval" when ever I say "range." Range has a specific meaning in statistics and therefore my use in this clip is not correct, range is a number not an interval. Other than that this is the best video ever recorded in the history of the world, or at least should be pretty useful if you forgot how to use the calculator to find the area under a normal curve for a specified interval.

Using Fathom - Mini tutorial

After you hit play, there is a little icon in the bottom right corner that if you click it you will get the full screen version of the video.

Measures of Central Tendency

Ti 83/84: Plotting Histograms

Using this data, follow the instructor as she makes a histogram on the graphing calculator!

70 56 48 53 52 66 48 36 49 28 35 58 62 45 60 38 73 45 51 56 51 46 39 56 32 44 60 51 44 63 50 46 69 53 70 33 54 55 52

Time Plot

A recent article points to the possibility of a double dip recession. Many economic indicators are monitored over time. For example, Unemployment and GDP Growth Rate.

United States GDP Growth Rate


People are also often interested in the value of a company over time. For example, right now it is estimated that Facebook's current value is $33.7 Billion.

Texting Top Teen Communication Link

Texting Top Teen Communication Link

Driver's Education, Does it work?

Who Knew?

So what is the Who? What? Why? When? Where? and hoW? For this data?

Sometimes it isn't about "Can it happen?" but "How likely is it to happen by chance?"

Today we did a simulation of a potential hiring discrimination problems. By repeating the simulation multiple times, and looking at the results of that simulation we can make a better judgement as to how likely one outcome is compared to another, than just by using intuition or guessing. For example, at East we collected data for a simulation involving selecting 8 captains via lottery from a group of 25 junior pilots, 15 of them were male pilots and 10 were female. Our results looked like this...

So we were able to determine that sure it could happen that the results of a fair lottery could be 5 females and 3 males selected to become captains. And not only "can it happen" (heck it "could" happen that all 8 selected are female) based on our results 5 females isn't really that surprising (but 8 sure would be). In AP Statistics we will continue to explore real life situations that and try to make sense of them. We will look at this problem (or one like it) in the future and go further than just running a simulation, we will look at the theoretical probability and actually calculate the theoretical probability of selecting 5 female captains, or 6, 7, and 8. This course will help you to interpret the world around you.

Welcome To Leyden AP Stats

What is your goal? "5"

How will you reach it? "Hard work"

Will you do it? "Yes we will"

I believe you.