Welcome back!
CHAPTER 9 TEST TUESDAY, JANUARY 24
Today (January 10th) we picked up the syllabus for the new semester, contributed more data to our collection of average penny ages, and investigated a problem related to Simpson's Paradox. We defined Simpson's Paradox as what happens when the "direction" of an association is reversed upon disaggregation of data. We paraphrased: When you break a set of data into components based on a lurking variable and the direction of the association switches you have a Simpson's Paradox.
Parents, ask your kids to show you the data. The situation is mind-blowing.
As an example, consider two students shooting baskets. Student A makes 40% of her two point shots and 30% of her three point shots. Student B makes 1/3 of her two point shots and 1/4 of her three point shots. They each attempt 1000 shots over the course of a season. Student A makes a higher percentage of her shots, right?
If student A shoots 40 two-pointers and 960 three pointers, then she makes 30.4% of her shots.
If student B shoots 900 two pointers and only 100 three pointers, then she makes 32.5% of her shots.
When the data are aggregated, student B has a higher success rate. When the shots are disaggregated by type of shot, student A has a higher success rate for each type of shot.
Behold, Simpson's Paradox.
Sampling Distributions Goals for the chapter:
- Define sampling distribution
- Contrast bias and variability
- Describe the sampling distribution of a sample proportion (shape, center, spread)
- Use a Normal approximation to solve probability problems involving the sampling distribution of a sample proportion
- Describe the sampling distribution of a sample mean
- State the central limit theorem
- Solve probability problems involving the sampling distribution of a sample mean
Sample proportion problems:
Section 9.1: 9.2, 9.5 a-b, 9.6, 9.7, 9.10, 9.14, SHOULD BE DONE BY 1/13
Section 9.2: 9.20, 9.21, 9.22, 9.23, 9.25, 9.26, 9.28, 9.29, 9.30 SHOULD BE DONE BY 1/17
Do not neglect the vocabulary. You should see that your understanding of the vocabulary affects your efficiency solving the problems above.
Sample mean problems will follow.
January 12, 2012
Yesterday and today we explored an example of statistical process control. We used JMP software to review the results of our data collection and saw how quality control people in the workplace would interpret the results.
Our next aspect to investigate is sampling distributions of proportions. Today we determined that the mean of the sample proportions is the true population proportion, and the standard deviation of the sample proportions is sqrt (pq/n). This will be approximately Normal when the conditions would make x, the number of successes, approximately Normal: np>= 10 and nq>=10. We also want the sample to be a small portion of the population, generally less than 10%. Enough of this theoretical stuff. . .we need to investigate!
Special HW due Friday: Spin a post 1970 penny on a flat surface until it stops naturally. Record whether it landed heads up. Repeat until you have 50 observations. Bring the number of heads up (successes) you have in the 50 tries. It will most likely NOT be 25.
Penny update: We have been calculating the average ages of samples of pennies in the classroom since last semester. The formula we should be using is age = 2011 minus the year of the penny. When we realized that many people had been calculating their average ages of the samples of pennies using the base year of 2012, we talked about how that would introduce bias into our results--the estimated age would be a year off from the way we calculated the first set of numbers, and the average sample ages would be bad estimates for the average age as of November 2011. We set aside the flawed data and started anew.
Tuesday, January 17, 2012
You should now understand the conditions under which the distribution of sample proportions will be approximately Normal and be able to compute the areas associated with related inequalities (like P(p-hat is less than .64)).
Wednesday we explore the Central Limit Theorem.
HW for section 9.3: 9.32, 9.33, 9.34, 9.38, 9.39, 9.40, 9.41, 9.45 DUE Thursday
HW for the Chapter review: 9.47, 9.49, 9.52, 9.54, 9.55, 9.58. DUE Friday
HW: find the loose pennies in your household, and create a histogram of their ages.
