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Webinar #2Daniel Carlson
Who is this voice?•Math Teacher
•Fruita Monument High School
•Not a “Stats” guy
Adobe Connect•Documents
•Chat
•Status/Attendee List
•Multiple Choice
Schedule4:10 – 5:00ish: Experimental Design5:00 – 6:00ish: Probability6:00 – 7:00: Sampling Distributions
Experimental Design
What is an experiment?
What is an experiment?•Researcher “imposes a treatment” on the experimental units.
What is an experiment?•Researcher “imposes a treatment” on the experimental units.
•Looking for Cause-and-Effect
What is an experiment?•Researcher “imposes a treatment” on the experimental units.
•Looking for Cause-and-Effect
•No treatment imposed = observational study
Control Groups
Control Groups•No Treatment (what happens naturally?)
Control Groups•No Treatment (what happens naturally?)
•Example: Bear meat seasoning
Control Groups•No Treatment (what happens naturally?)
•Example: Bear meat seasoning
•Placebo (what happens when you think you are receiving treatment)
Randomization
Randomization• Eliminate Extraneous Variables• Eliminates other variables that may be a part of the “cause and effect” that
you CANNOT see.
Randomization• Eliminate Extraneous Variables• Eliminates other variables that may be a part of the “cause and effect” that
you CANNOT see.
• Example: A new type of Maple Syrup• Control Group (Old Syrup)• Treatment Group (New Syrup)
Randomization• Eliminate Extraneous Variables• Eliminates other variables that may be a part of the “cause and effect” that
you CANNOT see.
• Example: A new type of Maple Syrup• Control Group (Old Syrup)• Treatment Group (New Syrup)
• Even out the variables we cannot see:• Hunger, smell/taste ability, how much you like Syrup to begin with, etc.
Blocking• Eliminate Extraneous Variables• Eliminates other variables that may be a part of the “cause and effect” that
you CAN see.
Blocking• Eliminate Extraneous Variables• Eliminates other variables that may be a part of the “cause and effect” that
you CAN see.
• Example: Canadians!
Blocking
Blocking (Matched Pairs)
Blocking (Matched Pairs)• Eliminate Extraneous Variables• Eliminates other variables that may be a part of the “cause and effect” that
you CAN see.
Blocking (Matched Pairs)• Eliminate Extraneous Variables• Eliminates other variables that may be a part of the “cause and effect” that
you CAN see.
• Matched Pairs – Each Subject gets both treatments and a difference is observed
Blocking (Matched Pairs)• Eliminate Extraneous Variables• Eliminates other variables that may be a part of the “cause and effect” that
you CAN see.
• Matched Pairs – Each Subject gets both treatments and a difference is observed
• Example: Smell/Taste Ability
MULTIPLE CHOICE
MC #1 (2 minutes and 15 seconds on AP Exam)
MC #1 (2 minutes and 15 seconds on AP Exam)
MC #2
MC #2
MC #3
MC #3
MC #4
MC #4
FREE RESPONSE
FREE RESPONSE #7a ( 5 minutes)
FREE RESPONSE #7a ( 5 minutes)
FREE RESPONSE #7b ( 5 minutes)
FREE RESPONSE #7b ( 5 minutes)
FREE RESPONSE #7c ( 2 minutes)
FREE RESPONSE #7c ( 2 minutes)
5 Minute Break
Probability
Probability
• SO MANY CONCEPTS!!• SO MANY FORMULAS!!• SO MUCH VOCAB!!
Probability
• SO MANY CONCEPTS!!• SO MANY FORMULAS!!• SO MUCH VOCAB!!
• LEARN A COUPLE THINGS REALLY WELL• RATHER THAN LOTS OF THINGS POORLY
Probability Problems involving 2 events
Probability Problems involving 2 events• 100 random people were polled• Event I – 80 people use the Internet daily• Event E – 60 people use E-mail daily• 50 people use both
Probability Problems involving 2 events• 100 random people were polled• Event I – 80 people use the Internet daily• Event E – 60 people use E-mail daily• 50 people use both
10
Probability Problems involving 2 events
What is the probability someone uses the internet OR e-mail daily?
10
Probability Problems involving 2 events
What is the probability someone uses the internet OR e-mail daily?
P(I or E) = P(I) +P(E) – P(I and E)
10
Probability Problems involving 2 events
What is the probability someone uses the internet OR e-mail daily?
P(I or E) = P(I) +P(E) – P(I and E)
P(I or E) = 80/100 + 60/100 – 50/100
10
Probability Problems involving 2 events
What is the probability someone uses the internet OR e-mail daily?
P(I or E) = P(I) +P(E) – P(I and E)
P(I or E) = 80/100 + 60/100 – 50/100
= .8 + .6 - .5 = .9
10
Probability Problems involving 2 events
What is the probability someone uses the internet OR e-mail daily?
P(I or E) = (30 + 50 + 10) /100
10
Probability Problems involving 2 events
What is the probability someone uses the internet OR e-mail daily?
P(I or E) = (30 + 50 + 10) /100 = 90/100 = .9
10
Probability Problems involving 2 events
What is the probability someone uses the e-mail GIVEN they use the internet?
10
Probability Problems involving 2 events
What is the probability someone uses the e-mail GIVEN they use the internet?
P(E|I) = P(E and I) / P(I)
10
Probability Problems involving 2 events
What is the probability someone uses the e-mail GIVEN they use the internet?
P(E|I) = P(E and I) / P(I)
P(E|I) = (50/100) / (80/100)
10
Probability Problems involving 2 events
What is the probability someone uses the e-mail GIVEN they use the internet?
P(E|I) = P(E and I) / P(I)
P(E|I) = (50/100) / (80/100)
P(E|I) = .5/.8 = .625
10
Probability Problems involving 2 events
What is the probability someone uses the e-mail GIVEN they use the internet?
10
Probability Problems involving 2 events
What is the probability someone uses the e-mail GIVEN they use the internet?
10
Probability Problems involving 2 events
What is the probability someone uses the e-mail GIVEN they use the internet?
P(E|I) = 50/80 = .625
10
Probability Problems involving 2 events• 100 random people were polled• Event I – 80 people use the Internet daily• Event E – 60 people use E-mail daily• 50 people use both
Probability Problems involving 2 events• 100 random people were polled• Event I – 80 people use the Internet daily• Event E – 60 people use E-mail daily• 50 people use both
I Not I total
E 50 10 60
Not E 30 10 40
total 80 20 100
Probability Problems involving 2 events
What is the probability someone uses the internet OR e-mail daily?
Probability Problems involving 2 events
What is the probability someone uses the internet OR e-mail daily?
I Not I totalE 50 10 60
Not E 30 10 40
total 80 20 100
Probability Problems involving 2 events
What is the probability someone uses the internet OR e-mail daily?
I Not I totalE 50 10 60
Not E 30 10 40
total 80 20 100
Probability Problems involving 2 events
What is the probability someone uses the internet OR e-mail daily?
I Not I totalE 50 10 60
Not E 30 10 40
total 80 20 100
P(I or E) = (80 + 60 – 50) / 100 = 90/100 = .9
Probability Problems involving 2 events
What is the probability someone uses the internet OR e-mail daily?
I Not I totalE 50 10 60
Not E 30 10 40
total 80 20 100
Probability Problems involving 2 events
What is the probability someone uses the internet OR e-mail daily?
I Not I totalE 50 10 60
Not E 30 10 40
total 80 20 100
P(I or E) = (50 + 30 + 10) / 100
Probability Problems involving 2 events
What is the probability someone uses the internet OR e-mail daily?
I Not I totalE 50 10 60
Not E 30 10 40
total 80 20 100
P(I or E) = (50 + 30 + 10) / 100 = 90/100 = .9
Probability Problems involving 2 events
• What is the probability someone uses the e-mail GIVEN they use the internet?
I Not I totalE 50 10 60
Not E 30 10 40
total 80 20 100
P(E|I) = 50/80 = .625
Independent Events
Independent Events
• Two events are Independent if knowing the outcome of one event does not change the probability of the other event occurring
Independent Events
• Two events are Independent if knowing the outcome of one event does not change the probability of the other event occurring
• Example: Rolling a 4 on a six sided dice and
flipping heads on a coin
CHECKING FOR INDEPENDENCE
Are using e-mail daily and using internet daily independent events?
I Not I total
E 50 10 60
Not E 30 10 40
total 80 20 100
CHECKING FOR INDEPENDENCE
Are using e-mail daily and using internet daily independent events?
I Not I total
E 50 10 60
Not E 30 10 40
total 80 20 100
?P(A) = P(A|B)
CHECKING FOR INDEPENDENCE
Are using e-mail daily and using internet daily independent events?
I Not I total
E 50 10 60
Not E 30 10 40
total 80 20 100
?P(A) = P(A|B)
?P(E) = P (E|I)
CHECKING FOR INDEPENDENCE
Are using e-mail daily and using internet daily independent events?
I Not I total
E 50 10 60
Not E 30 10 40
total 80 20 100
?P(A) = P(A|B)
?P(E) = P (E|I)
?60/100 = 50/80
CHECKING FOR INDEPENDENCE
Are using e-mail daily and using internet daily independent events?
I Not I total
E 50 10 60
Not E 30 10 40
total 80 20 100
?P(A) = P(A|B)
?P(E) = P (E|I)
?60/100 = 50/80
.6 ≠ .625
CHECKING FOR INDEPENDENCE
Are using e-mail daily and using internet daily independent events?
I Not I total
E 50 10 60
Not E 30 10 40
total 80 20 100
?P(A) = P(A|B)
?P(E) = P (E|I)
?60/100 = 50/80
.6 ≠ .625So these events are NOT INDEPENDENT
Independent Events
If two events are Independent then:
P(A and B) = P(A) x P(B)
Independent EventsIf two events are Independent then:
P(A and B) = P(A) x P(B)
• Example: Rolling a 4 on a six sided dice and
flipping heads on a coin
Independent EventsIf two events are Independent then:
P(A and B) = P(A) x P(B)
• Example: Rolling a 4 on a six sided dice and
flipping heads on a coin
P ( Rolling a 4 and Flipping Heads) = 1/6 x 1/2 = 1/12
Independent EventsIf two events are Independent then:
P(A and B) = P(A) x P(B)
• Example: Rolling a 4 on a six sided dice and
flipping heads on a coin
P ( Rolling a 4 and Flipping Heads) = 1/6 x 1/2 = 1/12 = .0833
FREE RESPONSE
FREE RESPONSE QUESTION #12
FREE RESPONSE QUESTION #12a (5 minutes)
FREE RESPONSE QUESTION #12a
FREE RESPONSE QUESTION #12b (5 minutes)
FREE RESPONSE QUESTION #12b
FREE RESPONSE QUESTION #12c (5 minutes)
FREE RESPONSE QUESTION #12c
MULTIPLE CHOICE (If time)
5 Minute Break
Sampling Distributions
Sampling Distributions
• Previous Problems dealt with looking at one person/event/thing
Sampling Distributions
• Previous Problems dealt with looking at one person/event/thing• Sampling Distributions deal with looking at multiple
persons/events/things
Sampling Distributions
• Previous Problems dealt with looking at one person/event/thing• Sampling Distributions deal with looking at multiple
persons/events/things
What does the distribution of all possible samples look like? rather than
What does the distribution of all possible individuals look like?
Sampling Distributions
• Almost any problem in STATS from this point forward involves either:
Sampling Distributions
• Almost any problem in STATS from this point forward involves either:
MEANSOR
PROPORTIONS
Applets – Mean Problems
Applets – Mean Problems
Mean Problem - Conditions
Random? Independent?Normal?
Mean Problem - Conditions
Random? Independent?Normal?
• The problem will usually state “random” or “SRS”
Mean Problem - Conditions
Random? Independent?Normal?
• The problem will usually state “random” or “SRS”
10n = Some #• Assume our population
is at least Some #
Mean Problem - Conditions
Random? Independent?Normal?
• The problem will usually state “random” or “SRS”
10n = Some #• Assume our population
is at least Some #
1. Parent population is ~Normal, so the sampling distribution is ~Normal.
2. n ≥30, so the CLT tells us our sampling distribution is ~Normal.
Applets – Proportion Problems
Applets – Proportion Problems
Proportion Problem - Conditions
Random? Independent?Normal?
Proportion Problem - Conditions
Random? Independent?Normal?
• The problem will usually state “random” or “SRS”
Proportion Problem - Conditions
Random? Independent?Normal?
• The problem will usually state “random” or “SRS”
10n = Some #• Assume our population
is at least Some #
Proportion Problem - Conditions
Random? Independent?Normal?
• The problem will usually state “random” or “SRS”
10n = Some #• Assume our population
is at least Some #
n(p) ≥ 10 & n(1-p) ≥ 10
If both are greater than 10, then our sampling distribution is ~Normal.
FREE RESPONSE
Free Response #9
Free Response #9a (4 minutes)
P (x ≥ 55.4) = .2119
Free Response #9b (2 minutes)
Free Response #9c (6 minutes)
P( ≥ 55.4) = .000973 ~ .0001
Free Response #9d (2 minutes)
MULTIPLE CHOICE
MC #4 (2 minutes and 15 seconds on AP Exam)
MC #4
MC #5
MC #5
MC #5
MC #5
MC #6
MC #6
MC #6
MC #6
MC #7
MC #7
MC #7
MC #7
QUESTIONS???
THANK YOU AND GOOD NIGHT!!
