1. Stephanie Daniel
AP Statistics

2. Agenda Introductions Nuts & Bolts: AP Exam & Pace FRQ: 2017 #6
Teaching Inference: PHANTOMS/PANIC
Nuts & Bolts: Grading, Textbook & Other Resources
Teaching Sampling Distributions: Dice & FRQ #6
Questions & Answers

3. Introductions Name School Years teaching AP Stats
Any thing(s) specific you want to take away from today?
Bonus: Fun Facts

4. Alonzo & Tracy Mourning Sr. High
About Me
Stephanie Daniel
Alonzo & Tracy Mourning Sr. High
6 years

5. Introductions Name School Years teaching AP Stats
Any thing specific you want to take away from today?
Bonus: Fun Facts

6. Nuts & Bolts
AP Exam Format
Pace & Calendar
Scope & Sequence

7. What’s on the Exam?
Exploring Data (20-30%): Describing patterns and departures from patterns (CH. 1-3) Sampling and Experimentation (10-15%): Planning and conducting a study (CH. 4) Anticipating Patterns (20-30%): Exploring random phenomena using probability and simulation (CH. 5-7) Statistical Inference (30-40%): Estimating population parameters and testing hypotheses (CH 8-12)

8. Exam Format Two 90 minute sections Reference Sheet and Calculator!
First section: 40 multiple choice questions
Second section: 6 free response questions (FRQs)
First 5 FRQs = 12 minutes each
FRQ # 6 : Investigative task for 30 minutes

9. Scoring Exam is scored out of 100 points. Each MC is worth 1.25 points
Each FRQ (#1-5) is worth 7.5 points
FRQ #6 is worth 15 points

10. FRQ Scoring Each question is scored from 1 to 4.
The raw score is then multiplied by to determined the scaled score.
The numerical score is derived from a series of:
Essentially Correct
Partially Correct
Incorrect

11. FRQ Scoring
Sample Scale for a 4 part question.

12. FRQ Scoring
Sample Scale for a 3 part question.

13. AP Stats 2017 Scores

14. District Scoring

15. Pace Goal End of 1st Quarter Finished Chapter 4 End of 2nd Quarter
End of 3rd Quarter
Finished Chapter 10
April 16
Start AP Review
May 17
AP Exam

16. Probability- just the basics!
Scope & Sequence
Probability- just the basics!
“Probability is the tool used for anticipating what the distribution of data should look like under a given model. Random phenomena are not haphazard: they display an order that emerges only in the long run and is described by a distribution. The mathematical description of variation is central to statistics. The probability required for statistical inference is NOT primarily axiomatic or combinatorial but is oriented toward using probability distributions to describe data.”

17. Probability
A. General Probability B. Combining independent random variables C. The normal distribution D. Sampling distributions

19. Probability General Probability
1. Interpreting probability, including long-run relative frequency interpretation
2. “Law of Large Numbers” concept
3. Addition rule, multiplication rule, conditional probability and independence
4. Discrete random variables and their probability distributions, including binomial and geometric
5. Simulation of random behavior and probability distributions
6. Mean (expected value) and standard deviation of a random variable, and linear transformation of a random variable

21. Inference ALWAYS at least one FRQ
Tests of Significance and Confidence Intervals

23. FRQ: 2017 #6
Mean Score: % of students earned a zero.

24. FRQ: 2017 #6 Chief Reader Comments:
For any probability calculation, students should provide justification that is easy to follow.
When asked to make a choice between options, make sure students explain why they are choosing what they are choosing, and why they are not choosing what they are not choosing.

25. Teaching Inference Chapters 8 to 12 40% of material on AP exam
PANIC & PHANTOMS

26. Confidence Interval
P-parameter A- assess conditions N- name interval (do math) I- interpret interval C- conclude in context

27. Example: Red Beads
Calculate and interpret a 90% confidence interval for the proportion of red beads in the container of 3000 beads. Mrs. Daniel claims 50% of the beads are red. Use your interval to comment on this claim. The sample proportion you found was red beads with a sample of 251 beads. z
.03
.04
.05
– 1.7
.0418
.0409
.0401
– 1.6
.0516
.0505
.0495
– 1.5
.0630
.0618
.0606
For a 90% confidence level, z* = 1.645

28. Example: Red Beads Parameter: p = true proportion of red beads
Assess Conditions:
Random: It is reasonable to assume that the sample was randomly collected.
Sample Size: Since both n 𝑝 ≥ 10 (251x = 106.9) and n(1 – 𝑝 ) ≥ 10 (251 x = 144.1) are both greater than 10, our sample size is large enough.
Independent: Since the sample of 251 is less than 10% of the population (3000 beads), it is reasonable to assume independence when sampling without replacement.

29. Example: Red Beads Name Interval: 1-proportion z-Interval Interval:
We are 90% confident that the interval from to will capture the true proportion of red beads.
statistic ± (critical value) • (standard deviation of the statistic)
/ *

30. Example: Red Beads Name Interval: 1-proportion z-Interval Interval:
We are 90% confident that the interval from to will capture the true proportion of red beads.

31. Example: Red Beads Conclude in Context:
It is pretty doubtful that Mrs. Daniel’s claim that 50% of the beads are red is true because 0.50 is not included within the interval.

32. Carrying Out a Significance Test
A basketball player who claims to be an 80% free-throw shooter. NBA scouts wanted to see the player in action. So, during the Combine, the player shot 50 free-throws, he made 32. (Consider it an SRS).
His sample proportion of made shots, 32/50 = 0.64, is much lower than what he claimed.
Does it provide convincing evidence against his claim?

33. Theory: One-Sample z Test for a Proportion
The z statistic has approximately the standard Normal distribution when H0 is true.

34. Theory: Test Statistic and P-value
A significance test uses sample data to measure the strength of evidence against H0.
The test compares a statistic calculated from sample data with the value of the parameter stated by the null hypothesis.
Values of the statistic far from the null parameter value in the direction specified by the alternative hypothesis give evidence against H0.
A test statistic measures how far a sample statistic diverges from what we would expect if the null hypothesis H0 were true.

35. Carrying Out a Significance TestP
 Parameters H
 Hypothesis A
 Assess Conditions N
 Name the Test T
 Test Statistic (Calculate) O
 Obtain P-value M
 Make a decision S
 State conclusion

36. Carrying Out a Significance Test
Parameters & Hypothesis
Parameter: p = the actual proportion of free throws the shooter makes in the long run.
Hypothesis:
H0: p = 0.80
Ha: p < 0.80

37. Carrying Out a Significance Test
Assess Conditions: Random, Normal & Independent.
Random
We can view this set of 50 shots as a simple random sample from the population of all possible shots that the player takes.
Normal
Assuming H0 is true, p = then np = (50)(0.80) = 40 and n (1 - p) = (50)(0.20) = 10 are both at least 10, so the normal condition is met.
Independent
In our simulation, the outcome of each shot does is determined by a random number generator, so individual observations are independent.

38. Carrying Out a Significance Test
Name the Test, Test Statistic (Calculate) & Obtain P-value
Name Test: One-proportion z-test
Z- score: -2.83
P- value:

39. Carrying Out a Significance Test
Name the Test
TINspire: Menu, 6: Statistics, 7: Stats Tests, 5: 1-Prop z Test

40. Carrying Out a Significance Test
Test Statistic (Calculate) & Obtain P-value

41. Carrying Out a Significance Test
Make a Decision & State the Conclusion
Make a Decision: P-value is Since the p-value is so small we reject the null hypothesis.
State the Conclusion: We have convincing evidence that the basketball player does not make 80% of his free throws.

42. Confidence Interval vs. Significance Test Which is better?

43. Nuts & Bolts, part 2 Grading Collect HW on days of tests/quizzes
Grade HW only for effort
2 to 3 test per quarter
4 to 5 quizzes per quarter
60% (plus) percent of grade from assessments
15% from notebook
20% from HW
5% from pop quizzes/random grades

44. Nuts & Bolts, part 2 1st Quarter Assessments 1.1 Quiz 1.2 Quiz
Chapter 1 Test
Chapter 2 Quiz
Chapter 3 Quiz
Chapter 2 & 3 Test
4.1 & 4.2 Quiz
Chapters 1 to 4 Test (double grade)

45. Nuts & Bolts, part 2 Textbook Resources CollegeBoard Resources
ExamView with bank
Alternative Examples
Pre-written Tests & Quizzes
Solutions Manual
CollegeBoard Resources
FRQs with Solutions & Commentary
Chief Grader Notes
Secured Exams
FRQ Index
Guided Notes- Daniel

46. Teaching Sampling Distributions
Sample, data, average, plot, repeat…
Each dot represents a sample’s average, not an individual!
Major connection to inference

48. Sample Distributions & Normality:

49. Sample Distributions & Normality:

50. Sample Distributions & Normality: HOW LARGE IS LARGE ENOUGH?
If the Population shape is….
Minimum Sample Size to assume Normal
Normal
Slightly Skewed 15
Heavily Skewed 30
Unknown

51. Dice Activity Roll your pair of dice 30 times
For each roll, record the sum
Place one blue dot for each roll
Then, find the average of all your rolls

52. FRQ: 2015 #6
Mean score: 1.08
Lots of zeros and twos.
Few 3s and 4s.

53. Questions???