1. AP STATISTICS Summer Institute 2016 Day 1
Lance Belin
JJ Pearce High School – Richardson, TX Years
AP Statistics Reader/Table Leader – College Board Years
Masters in Statistics - University of Texas - Dallas

2. Introductions: Name – School (location) – Years of Experience
Classroom procedures
Scope and Sequence – Calendar
Activities/Content support/Exam format/grading

3. APSI schedule
August 2, 2016
8:30 AM to 4:00 PM
Morning Break: 10:15 AM
Lunch: 11:30 -12:00
Afternoon Break: 2:00 PM
August 3, 2016
8:30 AM to 4:00 PM
Morning Break: 10:15 AM
Lunch: 11:30 -12:00
Afternoon Break: 2:00 PM
August 4, 2016
8:30 AM to 4:00 PM
Morning Break: 10:15 AM
Lunch: 12: :30
Afternoon Break: 2:00 PM
August 5, 2016
8:30 AM to 2:00 PM
Morning Break: 10:15 AM
Lunch: 12: :30

4. Highlight important topics from each of the 4 major contents areas
Exploring Data
Collecting Data
Probability
Statistical Inference
Provide activities that help illustrate these topics
Illustrate uses of graphing calculators, computer software, and applets in AP Statistics
Discuss the 2016 AP Exam in detail, including strategies for success on the AP Exam
Answer as many questions as possible from workshop participants

5. Insight to some of the commonly used AP Statistics textbooks
Access to many electronic files, including copies of lesson plans/student notes, copies of chapter tests, midterms and finals, examples of projects, a free-response question index, sortable by topic or textbook chapter, and the contents of this workshop pack (which means its OK to write on this one. These resources will be available at:
The Free Response portion of the 2016 AP Exam, including rubrics and sample papers
A College Board workshop packet that includes portions of the course description, the teacher’s guide, and the multiple choice questions from a released exam.
College Board Professional Development materials.

6. NMSI Resources
registration code for this school year is: NMSIstrive4a5 (and is case sensitive).
Mentoring – Request one!
Fall Training – 2-day training in the Fall on a Friday and Saturday, most dates are October and early November. Program managers and schools will provide those dates.
Mock Exam and Reading (Spring Training)– Program teachers are asked to administer a mock exam to every student in the spring. The Statistics mock exam for will be the 2015 Practice exam for the Multiple Choice and the 2015 Released Free Response Questions.

7. Page 5 – 6 : Teacher Recourses
Page 7 – 9 : Recruitment
Page 10-11: Classroom/Exam Preparation
..\ AP STATISTICS calendar.pdf

8. Page 4

9. Page 2
An Opening Activity - Hiring discrimination—it just won’t fly! (from Starnes/Yates/Moore, The Practice of Statistics for the AP Exam, 5e) An airline has just finished training 25 pilots—15 male and 10 female—to become captains. Unfortunately, only eight captain positions are available right now. Airline managers announce that they will use a lottery to determine which pilots will fill the available positions. The names of all 25 pilots will be written on identical slips of paper, placed in a hat, mixed thoroughly, and drawn out one at a time until all eight captains have been identified. A day later, managers announce the results of the lottery. Of the 8 captains chosen, 5 are female and 3 are male. Some of the male pilots who weren’t selected suspect that the lottery was not carried out fairly. Do these results provide convincing evidence that the lottery was unfair?

10. Page 2
An Opening Activity - Hiring discrimination—it just won’t fly! Lets Simulate!

11. 2014 Free Response # 2
Nine sales representatives, 6 men and 3 women, at a small company wanted to attend a national convention. There were only enough travel funds to send 3 people. The manager selected 3 people to attend and stated that the people were selected at random. The 3 people selected were women. There were concerns that no men were selected to attend the convention.
(a) Calculate the probability that randomly selecting 3 people from a group of 6 men and 3 women will result in selecting 3 women.

12. (b) Based on your answer to part (a), is there reason to doubt the manager’s claim that the 3 people were selected at random? Explain.

13. (c) An alternative to calculating the exact probability is to conduct a simulation to estimate the probability. A proposed simulation process is described below.
Each trial in the simulation consists of rolling three fair, six-sided dice, one die for each of the convention attendees. For each die, rolling a 1, 2, 3, or 4 represents selecting a man; rolling a 5 or 6 represents selecting a woman. After 1,000 trials, the number of times the dice indicate selecting 3 women is recorded.
  Does the proposed process correctly simulate the random selection of 3 women from a group of 9 people consisting of 6 men and 3 women? Explain why or why not.

14. Smelling Parkinson’s Disease PAGE 5 
As reported by the Washington Post ( Joy Milne of Perth, UK, smelled a “subtle musky odor” on her husband Les that she had never smelled before. At first, Joy thought maybe it was just from the sweat after long hours of work. But when Les was diagnosed with Parkinson’s 6 years later, Joy suspected the odor might be a result of the disease.
Scientists were intrigued by Joy’s claim and designed an experiment to test her ability to “smell Parkinson’s.” Joy was presented with 12 different shirts, each worn by a different person, some of whom had Parkinson’s and some of whom did not. The shirts were given to Joy in a random order and she had to decide whether each shirt was worn by a Parkinson’s patient or not.
1. Why would it be important to know that someone can smell Parkinson’s disease?
2. How many correct decisions (out of 12) would you expect Joy make if she couldn’t really smell Parkinson’s and was just guessing?
3. How many correct decisions (out of 12) would it take to convince you that Joy really could smell Parkinson’s?

15. 4. What claim were the researchers hoping to find evidence against
4. What claim were the researchers hoping to find evidence against? That is, what was their prior belief (null hypothesis) about the ability to smell Parkinson’s? 5. What claim were the researchers hoping to find evidence for? This is called the alternative hypothesis or the research hypothesis.

16. 6. Your instructor will hand you 12 cards (shirts) that have been shuffled into a random order. Don’t turn them over yet! On the back of some of them is “Parkinson’s” and on the back of others is “No Parkinson’s.” For each card, guess Parkinson’s or No Parkinson’s. Once you have made your guess, turn the card over and see if you were correct. Repeat this for each card and record the number of correct identifications (out of 12) below. NO
Parkinson’s NO
Parkinson’s
Parkinson’s NO
Parkinson’s NO
Parkinson’s NO
Parkinson’s
Parkinson’s
Parkinson’s
Parkinson’s NO
Parkinson’s
Parkinson’s NO
Parkinson’s

17. 7. Create a dotplot of the number of correct identifications with the rest of the class. Record the results below. 8. In the actual experiment, Joy identified 11 of the 12 shirts correctly. Based on the very small-scale simulation by you and your classmates, what proportion of the simulations resulted in 11 or more shirts correctly identified, assuming that the person was guessing? 9. The proportion you just calculated is a crude estimate of a true probability called a p-value. How might we improve our estimate of the true probability?

18. 2016 AP STATISTICS EXAM Question #4
a) WORK MUST BE SHOWN - Credit IS given to incorrect work as…
b) Independence
c) p-value

19. Student Sample 4 “A”

20. The Game of Greed Page 63 https://www.random.org/dice/?num=1

21. 2016 AP STATISTICS EXAM Question #1
CENTER - UNUSUAL - SHAPE - SPREAD
& CONTEXT

22. Student Sample A1

23. 2015 AP STATISTICS EXAM Question #1

24. 2015 AP STATISTICS EXAM Question #1

25. Statistical Inference Page 67-69 Match the type of inference with the Situation describe in 1-17 9 6 13 5 1 12 15 7 10 3 16 2 17 14 8 11 4

26. Confidence Intervals Page 71 P Parameter A Assumptions N Name the interval I Interval C Conclusion in context

27. Hypothesis Test P Parameter H Hypotheses A Assumptions N Name the test T Test statistic O Obtain P-value M Make decision S State conclusion in context

28. 2015 Free Response # 4 A researcher conducted a medical study to investigate whether taking a low-dose aspirin reduces the chance of developing colon cancer. As part of the study, 1,000 adult volunteers were randomly assigned to one of two groups. Half of the volunteers were assigned to the experimental group that took a low-dose aspirin each day, and the other half were assigned to the control group that took a placebo each day. At the end of six years, 15 of the people who took the low-dose aspirin had developed colon cancer and 26 of the people who took the placebo had developed colon cancer. At the significance level α = 0.05, do the data provide convincing statistical evidence that taking a low-dose aspirin each day would reduce the chance of developing colon cancer among all people similar to the volunteers?

32. Plickers
App

34. 2. What topic do you need the most support?
1. How many years of experience do you have teaching statistics? A. 0-1 B. 2-3 C. 4-5 D. 6+
2. What topic do you need the most support?
A. Probability B. Experimental Design
C. Inference D. Regression
3. A Linear regression inference with 12 students to determine if there exist a relationship between their SAT math scores and their AP Statistics scores is preformed. What is the number of DEGREES OF FREEDOM ?
A B C D

35. 4.

36. 5.

37. 6.

38. 7.

39. 8.

40. 9.

41. WHAT PERCENT OF THE EARTH IS COVERED WITH WATER?

42. One Proportion Significance Test
Is there evidence that the proportion of the earth that is covered with water is greater than 0.75
p = The true proportion of earth’s surface that is covered with water.
One Proportion
z – Test
H0: p = 0.75
Ha: p > 0.75
SRS – The data was collected randomly
Appr. Normal: n (0.75) ≥ AND n (1 – (0.75)) ≥ 10
Population of potential volleys is ≥ 10 · n
Since the P-Value is NOT less than α = we can NOT REJECT H0.
There is NO evidence to support that proportion of Earth covered by water is NOT equal to 75%
Since the P-Value is less than α = we REJECT H0 . There is sufficient evidence that the proportion of Earth covered by water is not 71%.

43. Page 38 Activity: How many Popsicle Sticks are in the Bag
Page 38 Activity: How many Popsicle Sticks are in the Bag? (aka The German Tank Problem)

44. AP statistics german tank Activity Your team of statisticians has 15 minutes to come up with a formula to estimate the number of Germans tanks that were used in WW2. The actual number is between 1 and Draw 5 serials numbers randomly from the envelope. 2. Develop a formula that you believe is a good method to estimate the actual number of German tanks. Use this formula and your 7 serial numbers to get your estimate. 3. Explain to the class your method. 4. What team is closest to the truth? 5. Collect 9 more sample of size 7 to get a total of 10 estimates of the number of German tanks. 6. Plot all 10 estimates on one dot plot. 7. On your paper, copy the dot plots for the results from the other teams. 8. Compare the dot plots for the class and answer the questions .

45. Which method produced the least bias?
Which method produced the least bias?
Which method produce the least variability?
Which method is the best method for estimating the number of tanks?

48. 2015 Free Response # 6
Corn tortillas are made at a large facility that produces 100,000 tortillas per day on each of its two production lines. The distribution of the diameters of the tortillas produced on production line A is approximately normal with mean 5.9 inches, and the distribution of the diameters of the tortillas produced on production line B is approximately normal with mean 6.1 inches. The figure below shows the distributions of diameters for the two production lines.
The tortillas produced at the factory are advertised as having a diameter of 6 inches. For the purpose of quality control, a sample of 200 tortillas is selected and the diameters are measured. From the sample of 200 tortillas, the manager of the facility wants to estimate the mean diameter, in inches, of the 200,000 tortillas produced on a given day. Two sampling methods have been proposed.
Method 1: Take a random sample of 200 tortillas from the 200,000 tortillas produced on a given day. Measure the diameter of each selected tortilla.
Method 2: Randomly select one of the two production lines on a given day. Take a random sample of 200 tortillas from the 100,000 tortillas produced by the selected production line. Measure the diameter of each selected tortilla.
a.) Will a sample obtained using Method 2 be representative of the population of all tortillas made that day, with respect to the diameters of the tortillas? Explain why or why not.

49. a.) Will a sample obtained using Method 2 be representative of the population of all tortillas made that day, with respect to the diameters of the tortillas? Explain why or why not.

50. 2015 Free Response # 6
b.) The figure below is a histogram of 200 diameters obtained by using one of the two sampling methods described. Considering the shape of the histogram, explain which method, Method 1 or Method 2, was most likely used to obtain such a sample.
c.) Which of the two sampling methods, Method 1 or Method 2, will result in less variability in the diameters of the 200 tortillas in the sample on a given day? Explain.

51. 2015 Free Response # 6
b.) The figure below is a histogram of 200 diameters obtained by using one of the two sampling methods described. Considering the shape of the histogram, explain which method, Method 1 or Method 2, was most likely used to obtain such a sample.
c.) Which of the two sampling methods, Method 1 or Method 2, will result in less variability in the diameters of the 200 tortillas in the sample on a given day? Explain.

52. 2015 Free Response # 6
Each day, the distribution of the 200,000 tortillas made that day has mean diameter 6 inches with standard deviation 0.11 inch.
d.) For samples of size 200 taken from one day’s production, describe the sampling distribution of the sample mean diameter for samples that are obtained using Method 1.
e.) Suppose that one of the two sampling methods will be selected and used every day for one year (365 days). The sample mean of the 200 diameters will be recorded each day. Which of the two methods will result in less variability in the distribution of the 365 sample means? Explain.

53. 2015 Free Response # 6
f. ) A government inspector will visit the facility on June 22 to observe the sampling and to determine if the factory is in compliance with the advertised mean diameter of 6 inches. The manager knows that, with both sampling methods, the sample mean is an unbiased estimator of the population mean. However, the manager is unsure which method is more likely to produce a sample mean that is close to 6 inches on the day of sampling. Based on your previous answers, which of the two sampling methods, Method 1 or Method 2, is more likely to produce a sample mean close to 6 inches? Explain.

54. Does the size of the population matter?
Consider the population of integers from 1 to Type them into L1 of your calculator.
What is the standard deviation? Is that or s ? Explain.
Let’s explore the standard deviation of the sampling distribution of the sample mean for SRSs of different sizes. Note: All samples will be selected without replacement.
We will calculate the mean and SD of the distribution three different ways for each sample:
STAT - EDIT - L ↑ - 2nd STAT→ OPS #5: seq(X,X,1,100,1)
STAT - CALC- #1: 1-Var Stats L1
MATH → PRB 8: randIntNoRep(1,100) – sto> – L2
“ n” – 2nd STAT→ OPS #3 sto> - dim(L2)

55. 10% RULE