AP STATS:

1. AP STATS: Take 10 minutes or so to complete your 7.1C quiz. When you finish, take a look at your quiz and your project and than read the page from How to Lie with Statistics and we’ll examine a recent ad related to this idea.

2. Some notes from the project • Very nicely done and some creative project ideas as well. • Make sure that you are explicit in how you conduct the experiment. Again someone should be able to read the study and replicate it. • No calculator speak. • Make sure that there is something quantitative that you are measuring in order to determine whether your results were significant.

3. Agenda • We will be covering 7.2 today and tomorrow. • We will review on Wednesday for the Chapter 6/7 Test. • It will be half multiple choice and half free response. • I will be putting up a lesson from an AP book online. It’s a good idea to read this as it is a summary of Chapter 6 and 7 (but more condensed and with some examples).

4. Video of the Day!How to Lie with Statistics? http://www.ispot.tv/ad/75Zn/verizon-map-gallery

5. A few reminders…. • P(X>1) • P(1<X<3) • P(X ≠2) • What does the area under the density curve always equal? • Mean is the balance point. • Median is the equal areas point

6. Reminders normal distribution

7. The mean of a random variable. • The mean of a random variable (X) is a mean that is weighted by the probability of each event occurring. It is a weighted average. • The mean of a probability distribution is denoted as mu-x. • We oftentimes call this the EXPECTED VALUE. The amount that we can expect to gain/lose ON AVERAGE in the long run, on each “play” of the game. Originally developed for the use of gambling (used frequently for things like insurance). • It is the sum of x

8. Lottery Example • Imagine the probability of winning the lotto is 1/1,000,000. • The payout if you win is $800,000. Lottery tickets cost a $1. What is the expected value of a lottery ticket?

9. Expected Value

10. Variance of a discrete random variable

11. Example

12. Sampling Distributions • One of the areas that this course is heading in is towards statistical inference. In other words, estimating a population parameter (like the population mean) from a sample. In other words, we will be approximating μ using a sample mean (x-bar). (We will study sampling distributions in Chapter 9.) • Say we wanted to find the mean height of all women in the US aged 18-24. We might take an SRS of women and use their sample mean to represent the true mean (μ) with a certain level of precision. • The LAW of LARGE NUMBERS the mean of the sample will approach the mean of the population (μ) as you increase the number of people sampled! ** this holds for ANY population (not just normal distributions)

13. Think flipping quarters. Or how casinos make money in the long run even though they might have a “bad” night.

14. A Psychological Shortcoming • Most people believe that short sequences of random events will show the same type of average behavior that we will only see in the long run. Casinos thrive off of this as it keeps gamblers gambling. • In other words, people falsely believe in a LAW OF SMALL NUMBERS which does not exist. • This has to do with the fallacy of the “hot hand” which I think we discussed…. What does “random” look like? This is the same idea as the GAMBLER’S FALLACY – i.e. people thinking that after 10 heads, a tail is more likely to “make-up for all the heads” and get the average back to 50%. The key is the long run. Remember the random events that are INDEPENDENT have no memory!

15. How large is a large number? • It depends. Particularly on the variability of the outcome. • The more variable the outcome, the more trials are needed for the sample mean to approach the actual mean.

16. HW • 7.24, 7.27, 7.28, 7.32, 7.34 • Read the article if the idea interests you. • www.rawbw.com/~deano/articles/aa121896.htm