1. AP STATISTICS Summer Institute 2016 Day 4
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. APSI schedule: August 5, 2016
8:30 AM to 2:00 PM
Morning Break: 10:15 AM
Lunch: 12: :30

5. Student Sample 2A1

6. Student Sample 2A1

7. Student Sample 2A1

8. Student Sample 2B

9. Student Sample 2E maybe

10. Student Sample 2 I

11. Blocking Page 47
What’s the Big Deal?

12. BLOCKING DOGS Page 47
The purpose of blocking is frequently described as “reducing variability.” However, this phrase carries little meaning to most beginning students of statistics. This activity, consisting of three rounds of simulation, is designed to illustrate what reducing variability really means in this context. In fact, students should see that a better description than “reducing variability” might be “attributing variability”, or “reducing unexplained variability”. The activity can be completed in a single 90-minute class or two classes of at least 45 minutes. For shorter classes you may wish to extend the simulations over two days. It is important that students understand not only what to do but also why they do what they do.

13.
FIX

15. Simulation 2 – Blocked by Breed
Data A B C D
Raw EX
-104
-101
-90
-87
-67
-60
-140
-132 Ca
-107
-108
-92
-98
-70
-71
-143 Co
-115
-110
-103
-105
-80
-79
-151
-154
ave.
New Ex
We must standardize the score to fairly make a comparison.

16. Simulation 2 – Blocked by Breed
Data A B C D
Raw EX
-104
-101
-90
-87
-67
-60
-140
-132 Ca
-107
-108
-92
-98
-70
-71
-143 Co
-115
-110
-103
-105
-80
-79
-151
-154
ave.
-107.5
-95.8
-71.2
-143.3
New Ex
average the 6 scores of your breed
subtract average from each score
We must standardize the score to fairly make a comparison.

17. Simulation 2 – Blocked by Breed
Data A B C D
Raw EX
-104
-101
-90
-87
-67
-60
-140
-132 Ca
-107
-108
-92
-98
-70
-71
-143 Co
-115
-110
-103
-105
-80
-79
-151
-154
ave.
-107.5
-95.8
-71.2
-143.3
New Ex
3.5
6.5
5.8
8.8
4.2
11.2
3.3
11.3 .5
-.5
3.8
-2.2
1.2 .2 .3
-7.5
-2.5
-7.2
-9.2
-8.8
-7.8
-7.7
-10.7
We must standardize the score to fairly make a comparison.

18. Simulation 2 – Blocked by Breed

19. Simulation 2 – Blocked by Breed

20. Simulation 3 – Blocked by Clinic
Data
Paw
Pooch
Tree
Bark
Raw EX
-103
-89
-60
-140
-88
-66
-139 Ca
-98
-95
-105
-108
-70
-136
-69 Co
-81
-153
-104
-151
-115
-110
-101
ave.
New Ex

21. Simulation 3 – Blocked by Clinic
Data
Paw
Pooch
Tree
Bark
Raw EX
-103
-89
-60
-140
-88
-66
-136 Ca
-98
-95
-105
-108
-70
-69 Co
-81
-153
-104
-151
-115
-110
-101
ave.
-103.2
-111.3
-97.5
-105.8
New Ex

22. Simulation 3 – Blocked by Clinic
Data
Paw
Pooch
Tree
Bark
Raw EX
-103
-89
-60
-140
-88
-66
-136 Ca
-98
-95
-105
-108
-70
-69 Co
-81
-153
-104
-151
-115
-110
-101
ave.
-103.2
-111.3
-97.5
-105.8
New Ex .2
14.2
51.3
-28.7
9.5
31.5
-30.2
-34.2
5.2
8.2
6.3
3.3
27.5
-38.5
-2.2
36.8
22.2
-49.8
7.3
-39.7
-17.5
-12.5
4.8
24.8

23. Simulation 3 – Blocked by Clinic

24. Simulation 3 – Blocked by Clinic

26. Blocking in Experiments: Online SAT schools (From TPS 5e ATE) Page 30

27. Two Sample vs. Matched Pairs
Should I perform a two sample t-test or a matched pairs t-test?  This is the ultimate question in AP Statistics, as far as I have seen. Today, I’ll elaborate on the differences between the two tests and list the characteristics of each test.
The conditions for a Matched pairs t-test:
Randomization: The 2 data sets must come from a randomized sample or a well-designed randomized experiment.
Independence: The two data sets are NOT INDEPENDENT of each other. They come from the same population. The INDIVIDUAL DIFFERENCES ARE INDEPENDENT as long as there is nothing to influence the observed differences. Ensure that ten times the sample size is less than the population size.
Normality: The central limit theorem applies when the sample size is greater than or equal to 30. For sample sizes that are less than 30 but more than 15, use t procedures only if there are no outliers or strong skewness.

28. According to my personal experiences, for the majority of the time, matched pair tests involve the words “pre” and “post”. DIFFERENT treatments are imposed on SIMILAR SUBJECTS.  A matched pairs t-test asks for the MEAN DIFFERENCE.  An example of a matched pairs t-test question would be the following: Determine if the unit 1 test scores are significantly different than the pre test scores for a class of students.

29. The conditions for a 2 Sample t-test:
Randomization: see above
Independence: Because inferences are made on two different populations, make sure that 10 times the sample size is less than the population size in each population.
Normality: see above
The key points of 2 sample t-test problems are as follows: the goal of the inference is to compare responses of two treatments (on two populations) or to compare characteristics of two populations; we have separate samples from each treatment or population; and the responses of each group are independent of those in the other group. Thus, a 2 sample t-test analyzes the DIFFERENCE BETWEEN TWO MEANS.  An example of a sample 2 sample t-test would be as follows: Is Tylenol significantly more effective on old people than on young people?

30. MATCHED PAIRS EXPERIMENT Are YOU easily Distracted?
In a minute you will see a Slide that contains 25 objects. You will have 20 seconds to study the slide and recall as many of the objects as possible. At the end of the 20 sec. the objects will disappear and I will ask you to write down as many as you can remember.
READY?????
μi = The true mean number of recalled objects…
μ1 = Not Distracted μ2 = Distracted

32. STOP

33. 1 Point for each correctly identified object
On a piece of paper write down as many as you remember.
SCORING
1 Point for each correctly identified object
apple
banana
bus
camera
cassette tape
cat
computer
earth
football
hammer
haystack
horse
Icecream
iphone
JJ Pearce HS
M TV
McDonald's
Mr. Potato Head
Mustang car
pencil
phone book
Pittsburg Steelers Logo
Space Shuttle
stapler
sun

35. Round 2

56. STOP

57. 1 Point for each correctly identified object
On a piece of paper write down as many as you remember.
SCORING
1 Point for each correctly identified object
Best Buy Logo
bicycle
cards
dollar bill
Flag
Ford Truck
Green Bay Packers
ipod
Laptop Computer
Mr. Belin
NASA Logo
Nike Shoe
orange
shovel
sissors
Snooky
Statue of Liberty
stop sign
Superman
tank
trash can
Tree
White House
window
Xbox 360 Logo

59. μd= The true mean DIFFERENCE in number of objects recalled (Not Distracted – Distracted)
Matched Pairs
t – test
H0: μd = 0
Ha: μd > 0
SRS – It needs to be
Approximately Normal Distribution – Graph
Since the P-Value is less than α = there is strong evidence to REJECT H0 . Distractions greatly impede the ability to recall objects.
Since the P-Value is Not less than α = there insufficient evidence to REJECT H0 . There is insufficient evidence that Distractions greatly impede the ability to recall objects.

60. Do the data provide convincing evidence that, on average, women pay more than men in the county for the same car model?

61. The 2014 AP Statistics Free Response #5 had a really tricky matched pairs t-test question. The reason for its trickiness was that we were not making an inference on human subjects, but on cars.  Data for men and women were given.  So, students probably presumed that the question was a 2 sample t-test asking them to determine if there was a significant difference between the amount of money spent on cars for men and women.  Students probably did not realize that for each car, both men’s and women’s average purchase prices were given.  The subjects were cars and the “treatments” can be considered men and women.

65. 2016 AP STATISTICS EXAM Question #3

66. Student Response 3A

67. Student Response 3A (c)

68. Student Response 3B

69. Student Response 3C

70. 2015 Free Response Question #5 Page 17

71. COMBINING INDEPENDENT RANDOM VARIABLES:
PART I PAGE 38

72. Page 37

73. COMBINING INDEPENDENT RANDOM VARIABLES: page 36
1. Construct the probability distribution for each of the members die.
2. Using your distributions from above, calculate the mean of each die.
 3. Using your distributions from above, calculate the standard deviation of each die.
4. A typical activity for dice is to roll them and add them together. Write out the sample space for the combination of your two dice.
5. Using your sample space, calculate and construct the probability distribution for the sum of the numbers on each of your die. Remember that the die are independent of each other, so rolling a 3 on a four-sided die and an 8 on a twelve-sided die, for a sum of 11 die is (¼)(1/8) = 1/48

75. Chips Ahoy used to advertise “1000 Chips in Every Bag!”
I CLAIM its not even Half (500 chips).
How would YOU do a significance test to test this?
What issues do you think would arise and how would you over come them?
1000 Chips in Every Bag!

76. Chips Ahoy used to advertise “1000 Chips in Every Bag
Chips Ahoy used to advertise “1000 Chips in Every Bag!” With X cookies in each bag, that meant that there was a population average of ???? chips per cookie. Because there was a suspicion of LESS than ???? chip/cookie the company disregarded the ad. Test this claim by crumbling cookies and counting the number of chips in each.
a.) Is there evidence to support the company’s decision. Gather evidence and Conduct a Significance test.
b.) Estimate the true # of chips in the bag by finding a 95% Confidence Interval for the true # of chips per cookie and then multiply it by X.
c.) Eat your evidence.
1000 Chips in Every Bag!

77. B Page 9

78. Which data set is modeled best by a line? Page 16

79. B Page 9

80. APSI Survey: 

81. Cumulative Relative Frequency Histogram
Med = 50%=0.5
Q1 = 25%=0.25 72
70.5
73.5
HEIGHTS IN INCHES OF A MEN BB TEAM

82. HW: Page 95; 27,28,34-36
i.) 30, 30, 60, 90, 90
ii.) 30, 50, 60, 70, 90