webinar #2 daniel carlson. who is this voice? math teacher fruita monument high school not a...
TRANSCRIPT
![Page 1: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/1.jpg)
Webinar #2Daniel Carlson
![Page 2: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/2.jpg)
Who is this voice?•Math Teacher
•Fruita Monument High School
•Not a “Stats” guy
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Adobe Connect•Documents
•Chat
•Status/Attendee List
•Multiple Choice
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Schedule4:10 – 5:00ish: Experimental Design5:00 – 6:00ish: Probability6:00 – 7:00: Sampling Distributions
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Experimental Design
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What is an experiment?
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What is an experiment?•Researcher “imposes a treatment” on the experimental units.
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What is an experiment?•Researcher “imposes a treatment” on the experimental units.
•Looking for Cause-and-Effect
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What is an experiment?•Researcher “imposes a treatment” on the experimental units.
•Looking for Cause-and-Effect
•No treatment imposed = observational study
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Control Groups
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Control Groups•No Treatment (what happens naturally?)
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Control Groups•No Treatment (what happens naturally?)
•Example: Bear meat seasoning
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Control Groups•No Treatment (what happens naturally?)
•Example: Bear meat seasoning
•Placebo (what happens when you think you are receiving treatment)
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Randomization
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Randomization• Eliminate Extraneous Variables• Eliminates other variables that may be a part of the “cause and effect” that
you CANNOT see.
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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)
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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.
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Blocking• Eliminate Extraneous Variables• Eliminates other variables that may be a part of the “cause and effect” that
you CAN see.
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Blocking• Eliminate Extraneous Variables• Eliminates other variables that may be a part of the “cause and effect” that
you CAN see.
• Example: Canadians!
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Blocking
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Blocking (Matched Pairs)
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Blocking (Matched Pairs)• Eliminate Extraneous Variables• Eliminates other variables that may be a part of the “cause and effect” that
you CAN see.
![Page 24: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/24.jpg)
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
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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
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MULTIPLE CHOICE
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MC #1 (2 minutes and 15 seconds on AP Exam)
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MC #1 (2 minutes and 15 seconds on AP Exam)
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MC #2
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MC #2
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MC #3
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MC #3
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MC #4
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MC #4
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FREE RESPONSE
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FREE RESPONSE #7a ( 5 minutes)
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FREE RESPONSE #7a ( 5 minutes)
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FREE RESPONSE #7b ( 5 minutes)
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FREE RESPONSE #7b ( 5 minutes)
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FREE RESPONSE #7c ( 2 minutes)
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FREE RESPONSE #7c ( 2 minutes)
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5 Minute Break
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Probability
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Probability
• SO MANY CONCEPTS!!• SO MANY FORMULAS!!• SO MUCH VOCAB!!
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Probability
• SO MANY CONCEPTS!!• SO MANY FORMULAS!!• SO MUCH VOCAB!!
• LEARN A COUPLE THINGS REALLY WELL• RATHER THAN LOTS OF THINGS POORLY
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Probability Problems involving 2 events
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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
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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
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Probability Problems involving 2 events
What is the probability someone uses the internet OR e-mail daily?
10
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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
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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
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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
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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
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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
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Probability Problems involving 2 events
What is the probability someone uses the e-mail GIVEN they use the internet?
10
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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
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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
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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
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Probability Problems involving 2 events
What is the probability someone uses the e-mail GIVEN they use the internet?
10
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Probability Problems involving 2 events
What is the probability someone uses the e-mail GIVEN they use the internet?
10
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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
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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
![Page 63: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/63.jpg)
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
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Probability Problems involving 2 events
What is the probability someone uses the internet OR e-mail daily?
![Page 65: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/65.jpg)
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
![Page 66: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/66.jpg)
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
![Page 67: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/67.jpg)
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
![Page 68: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/68.jpg)
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
![Page 69: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/69.jpg)
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
![Page 70: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/70.jpg)
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
![Page 71: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/71.jpg)
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
![Page 72: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/72.jpg)
Independent Events
![Page 73: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/73.jpg)
Independent Events
• Two events are Independent if knowing the outcome of one event does not change the probability of the other event occurring
![Page 74: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/74.jpg)
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
![Page 75: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/75.jpg)
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
![Page 76: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/76.jpg)
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)
![Page 77: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/77.jpg)
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)
![Page 78: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/78.jpg)
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
![Page 79: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/79.jpg)
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
![Page 80: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/80.jpg)
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
![Page 81: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/81.jpg)
Independent Events
If two events are Independent then:
P(A and B) = P(A) x P(B)
![Page 82: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/82.jpg)
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
![Page 83: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/83.jpg)
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
![Page 84: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/84.jpg)
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
![Page 85: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/85.jpg)
FREE RESPONSE
![Page 86: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/86.jpg)
FREE RESPONSE QUESTION #12
![Page 87: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/87.jpg)
FREE RESPONSE QUESTION #12a (5 minutes)
![Page 88: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/88.jpg)
FREE RESPONSE QUESTION #12a
![Page 89: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/89.jpg)
FREE RESPONSE QUESTION #12b (5 minutes)
![Page 90: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/90.jpg)
FREE RESPONSE QUESTION #12b
![Page 91: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/91.jpg)
FREE RESPONSE QUESTION #12c (5 minutes)
![Page 92: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/92.jpg)
FREE RESPONSE QUESTION #12c
![Page 93: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/93.jpg)
MULTIPLE CHOICE (If time)
![Page 94: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/94.jpg)
5 Minute Break
![Page 95: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/95.jpg)
Sampling Distributions
![Page 96: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/96.jpg)
Sampling Distributions
• Previous Problems dealt with looking at one person/event/thing
![Page 97: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/97.jpg)
Sampling Distributions
• Previous Problems dealt with looking at one person/event/thing• Sampling Distributions deal with looking at multiple
persons/events/things
![Page 98: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/98.jpg)
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?
![Page 99: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/99.jpg)
Sampling Distributions
• Almost any problem in STATS from this point forward involves either:
![Page 100: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/100.jpg)
Sampling Distributions
• Almost any problem in STATS from this point forward involves either:
MEANSOR
PROPORTIONS
![Page 101: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/101.jpg)
Applets – Mean Problems
![Page 102: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/102.jpg)
Applets – Mean Problems
![Page 103: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/103.jpg)
Mean Problem - Conditions
Random? Independent?Normal?
![Page 104: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/104.jpg)
Mean Problem - Conditions
Random? Independent?Normal?
• The problem will usually state “random” or “SRS”
![Page 105: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/105.jpg)
Mean Problem - Conditions
Random? Independent?Normal?
• The problem will usually state “random” or “SRS”
10n = Some #• Assume our population
is at least Some #
![Page 106: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/106.jpg)
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.
![Page 107: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/107.jpg)
Applets – Proportion Problems
![Page 108: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/108.jpg)
Applets – Proportion Problems
![Page 109: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/109.jpg)
Proportion Problem - Conditions
Random? Independent?Normal?
![Page 110: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/110.jpg)
Proportion Problem - Conditions
Random? Independent?Normal?
• The problem will usually state “random” or “SRS”
![Page 111: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/111.jpg)
Proportion Problem - Conditions
Random? Independent?Normal?
• The problem will usually state “random” or “SRS”
10n = Some #• Assume our population
is at least Some #
![Page 112: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/112.jpg)
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.
![Page 113: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/113.jpg)
FREE RESPONSE
![Page 114: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/114.jpg)
Free Response #9
![Page 115: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/115.jpg)
Free Response #9a (4 minutes)
![Page 116: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/116.jpg)
![Page 117: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/117.jpg)
![Page 118: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/118.jpg)
P (x ≥ 55.4) = .2119
![Page 119: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/119.jpg)
Free Response #9b (2 minutes)
![Page 120: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/120.jpg)
![Page 121: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/121.jpg)
Free Response #9c (6 minutes)
![Page 122: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/122.jpg)
![Page 123: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/123.jpg)
![Page 124: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/124.jpg)
![Page 125: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/125.jpg)
![Page 126: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/126.jpg)
![Page 127: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/127.jpg)
![Page 128: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/128.jpg)
P( ≥ 55.4) = .000973 ~ .0001
![Page 129: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/129.jpg)
Free Response #9d (2 minutes)
![Page 130: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/130.jpg)
![Page 131: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/131.jpg)
MULTIPLE CHOICE
![Page 132: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/132.jpg)
MC #4 (2 minutes and 15 seconds on AP Exam)
![Page 133: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/133.jpg)
MC #4
![Page 134: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/134.jpg)
MC #5
![Page 135: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/135.jpg)
MC #5
![Page 136: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/136.jpg)
MC #5
![Page 137: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/137.jpg)
MC #5
![Page 138: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/138.jpg)
MC #6
![Page 139: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/139.jpg)
MC #6
![Page 140: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/140.jpg)
MC #6
![Page 141: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/141.jpg)
MC #6
![Page 142: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/142.jpg)
MC #7
![Page 143: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/143.jpg)
MC #7
![Page 144: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/144.jpg)
MC #7
![Page 145: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/145.jpg)
MC #7
![Page 146: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/146.jpg)
QUESTIONS???
![Page 147: Webinar #2 Daniel Carlson. Who is this voice? Math Teacher Fruita Monument High School Not a “Stats” guy](https://reader034.vdocuments.site/reader034/viewer/2022051620/56649ee55503460f94bf3ee4/html5/thumbnails/147.jpg)
THANK YOU AND GOOD NIGHT!!