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Transcript of + Lab 4: Expert Groups 008 Group 1DavidGuillermoLaurenMallory 2JonathonVivianKristen 3Alexander...
+Lab 4: Expert Groups 008
Group
1 David Guillermo Lauren Mallory
2 Jonathon Vivian Kristen
3 Alexander B
Berkley Melanie Eddie
4 Richard Keltan Heather Skriba
5 Chris Maya Heather Smallwood
Alexander W
6 Mollie Brad Hannah
7 Erin Howie Anna Pujiao
8 Jessica Elliot DominicPlease sit with your group and do not log on the computers.
+Lab 4: Expert Groups (010)
Group
1 Brad So Yun Kris Molly
2 Jacob Alex Peter
3 Drake Danny Derek Andrew
4 Ashley Michelle Emily R
5 Emily F Matt Matan Grant
6 Madeline Renee Taylor
7 Katie Mardie Chrissy Gordon
8 Emily J Joseph Supriya
Please sit with your group and do not log on the computers.
+
STATS 250 Lab 3
Julie GhekasSeptember 22, 2014
Please don’t log in. We will not be using the computers, and we will be moving.
+Schedule
Lab 2 Wrap Up
Probability
Warm Up
Lab 3
Cool Down/iClicker Questions
Example Exam Question
+Practice Homework Comments
Only 80% of you turned in homework
As a class, you struggled the most with Q3
Estimating the percent of time over 90 minutes Show work Count frequencies over 90/total (272) *100
Graph Describe the shape In context With values
+Time Plots
Looks can be misleading Has a time variable on the x-axis
Checking for stability to check independently distributed assumption Trend means no trend, no seasonal variation, and no
pattern in variation
Should make histogram only when the time plot shows stability
+Lab 2: Time-Dependent Data
1949
1952
1955
1958
1961
1964
1967
1970
1973
1976
1979
1982
1985
1988
1991
1994
1997
2000
2003
2006
2009
2012
0
50
100
150
200
250
300
350
400
Average Yards Earned by UM fb
rush yards/gamepass yards/game
Season
Avera
ge G
am
e Y
ard
age
+Lab 2: Time-Dependent Data
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 470
50
100
150
200
250
300
Pass yards by Game 1981-1984
Sequence Number
Overa
ll p
ass y
ard
s/g
am
e
+QQ Plots
Is the sample drawn from a normally distributed population?
We want a roughly straight line.
Remember that we are making inferences about the population.
Shows the relationship between quantiles (Q) of observed data and quantiles (Q) of expected of a normal distribution.
+Probability
Three distributions that you have learned: Normal X~N(μ, σ)
Standard Normal X~N(0, 1) Binomial X~Binom(n, p)
Normal Approximation for Binomial Distribution Uniform X~Unif(a,b)
Two probability definitions that you have learned: Independent events Mutually exclusive events
+Probability
Rules from Yellow Formula Card
To calculate the probability of an observation by hand: Draw distribution curve Shade appropriate area of the curve Calculate the probability using z-table if normal distribution Calculate area under the curve if continuous random
variable Add the individual probabilities if discrete random variable
+Probability Calculations
Empirical rule can answer some probability questions
What if empirical rule fails because observation is not exactly on a standard deviation from the mean?
Example: random variable IQ scores for Americans IQ~N(100,20) P(IQ>125) Draw the curve, and shade the area Find the z-score, and use Table A1 on your formula card
+Probability Calculations: Table A1
Use only with Normal distributions
Provides probabilities for a standard normal curve
Gives area to the left of a z-score
Let’s try using Table A1
+Probability Calculations
Can use R to calculate probability
Canvas -> R Tutorials -> Probabilities in R -> Download file under Necessary Files header
Open the downloaded prob-calc.rdata
Type prob( ) to start the program
Type q to quit
Calculate P(Z<1.2)
+Probability Calculations
Can use R to calculate probability
Canvas -> R Tutorials -> Probabilities in R -> Download file under Necessary Files header
Open the downloaded prob-calc.rdata
Type prob( ) to start the program
Type q to quit
Calculate P(Z<1.2) = 0.8849
+Probability Calculations
What if the distribution is Uniform instead of Normal?
Example: IQ~U(100, 200)
Draw curve, and shade desired region
Find the area of rectangle(s) Area=length*width
+Probability Calculations
If discrete random variable, then sum up all of the individual probabilities
Binomial distribution is a discrete distribution Binomial counts the number of successful trials with equal
probability p if you perform n trials
Consider flipping a coin 10 times. If X is a random variable for the number of heads, X~Bin(10, 0.5), assuming the coin is fair
+Lab 4: Expert Groups 008
Group Problem Float
1 1 David Guillermo Lauren Mallory
2 1 Jonathon Vivian Kristen
3 2 Alexander B
Berkley Melanie Eddie
4 2 Richard Keltan Heather Skriba
5 3 Chris Maya Heather Smallwood
Alexander W
6 3 Mollie Brad Hannah
7 4 Erin Howie Anna Pujiao
8 4 Jessica Elliot DominicDon’t worry about the R-script part of Problem 4
Change Question 3 part c to “Interpret the z-score.”
+Lab 4: Expert Groups (010)
Group Problem Float
1 1 Brad So Yun Kris Molly
2 1 Jacob Alex Peter
3 2 Drake Danny Derek Andrew
4 2 Ashley Michelle Emily R
5 3 Emily F Matt Matan Grant
6 3 Madeline Renee Taylor
7 4 Katie Mardie Chrissy Gordon
8 4 Emily J Joseph Supriya
Don’t worry about the R-script part of Problem 4
Change Question 3 part c to “Interpret the z-score.”
+Lab 4: Share Groups 008
Problem 1 2 3 4
1 David Alexander B Chris Erin
2 Guillermo Berkley Maya Howie
3 Lauren Melanie Heather Smallwood
Anna
4 Jonathon Richard Mollie Pujiao
5 Vivian Keltan Brad Jessica
6 Kristen Heather Skriba
Hannah Elliot
7 Mallory Eddie Alexander W Dominic
Don’t worry about the R-script part of Problem 4
+Lab 4: Share Groups (010)
Problem 1 2 3 4
1 Brad Drake Emily F Katie
2 So Yun Danny Matt Mardie
3 Kris Derek Matan Chrissy
4 Molly Andrew Grant Gordon
5 Jacob Ashley Madeline Emily J
6 Alex Michelle Renee Joseph
7 Peter Emily R Taylor Supriya
Don’t worry about the R-script part of Problem 4
+Lab 4: Problem 1
a. What is the probability that a randomly selected person smiled?
b. To check if smiling status is independent of gender, (a) should be compared to:P(smiled and male) P(smiled given male)P(male given smiled) P(male)
c. Find (b).
d. Do smiling status and gender appear to be independent?
Smile No Smile Total
1=Male 3269 3806 7075
2=Female 4471 4278 8749
Total 7740 8084 15824
+Lab 4: Problem 2
Suppose the probability of 7 days is twice as likely as the probability of 8 days. Complete the probability distribution.
What is the expected number of days for the longest trip? Include symbol, value, and units.
X 4 5 6 7 8
Probability 0.10 0.20 0.25
+Lab 4: Problem 3
Which are correct? On average, the number of hours spent studying
statistics varied from the mean by about 3.5 hours. The average distance between the number of hours
spent studying statistics is roughly 3.5 hours. The average number of hours spent studying statistics
is about 3.5 hours away from the mean.
+Lab 4: Problem 3
Assume the mean is 10 and the standard deviation is 3.5. Julie studies for about 6 hrs/week. What is her z-score?
Male students have a lower mean and larger standard deviation than female students. Jake’s response corresponds to z=2.1. Can we compare scores?
+Lab 4: Problem 4
Assume that for Chem, the mean is 12 and the standard deviation is 3.
What is the probability that a randomly selected Chemistry student studies between 16 and 20 hours per week?
+Lab 4: Problem 4
Assume that for Chem, the mean is 12 and the standard deviation is 3.
Jing learns that she is in the top 30%. This means that Jing must study at least how many hours per week?
+Cool Down/iClicker
If the time to wait for pharmacy help has a uniform distribution from 0 to 30 minutes, then 33% of the customers are expected to wait for more than 20 minutes.
A. True
B. False
+Cool Down/iClicker
If the time to wait for pharmacy help has a uniform distribution from 0 to 30 minutes, then 33% of the customers are expected to wait for more than 20 minutes.
A. True
B. False
+Cool Down/iClicker
If X has a Binomial(50, 0.7) distribution, then the criteria to use the normal approximation are met.
A. True
B. False
+Cool Down/iClicker
If X has a Binomial(50, 0.7) distribution, then the criteria to use the normal approximation are met.
A. True
B. False
+Cool Down/iClicker
68% of all test scores will fall within one standard deviation of the mean test score.
A. True
B. False
+Cool Down/iClicker
68% of all test scores will fall within one standard deviation of the mean test score.
A. True
B. False
+Cool Down/iClicker
Police report that 78% of drivers stopped on suspicion of drunk driving are given a breath test, 36% are given a blood test, and 22% are given both tests. Do the police administer these two tests independently?
A. True
B. False
+Cool Down/iClicker
Police report that 78% of drivers stopped on suspicion of drunk driving are given a breath test, 36% are given a blood test, and 22% are given both tests. Do the police administer these two tests independently?
A. True
B. False
+iClicker
If the variable X is strongly skewed to the right with a mean of 80 and a standard deviation of 2, then 95% of the values are expected to be between 76 and 84.
A. True
B. False
+iClicker
If the variable X is strongly skewed to the right with a mean of 80 and a standard deviation of 2, then 95% of the values are expected to be between 76 and 84.
A. True
B. False
+iClicker
Suppose the amount spent by students on materials for summer half term has approx a normal, bell-shaped distribution. Mean amount spent was $300 and standard deviation was $100.
About 68% of the students spent between ____.
A. $300 and $400
B. $200 and $400
C. $100 and $500
D. $266 and $334
+iClicker
Suppose the amount spent by students on materials for summer half term has approx a normal, bell-shaped distribution. Mean amount spent was $300 and standard deviation was $100.
About 68% of the students spent between ____.
A. $300 and $400
B. $200 and $400
C. $100 and $500
D. $266 and $334
+iClicker
Suppose the amount spent by students on materials for summer half term has approx a normal, bell-shaped distribution. Mean amount spent was $300 and standard deviation was $100.
What amount spent on materials has a standardized score of 0.5?
A. $150
B. $250
C. $300.50
D. $350
+iClicker
Suppose the amount spent by students on materials for summer half term has approx a normal, bell-shaped distribution. Mean amount spent was $300 and standard deviation was $100.
What amount spent on materials has a standardized score of 0.5?
A. $150
B. $250
C. $300.50
D. $350
+iClicker
Suppose the amount spent by students on materials for summer half term has approx a normal, bell-shaped distribution. Mean amount spent was $300 and standard deviation was $100.
Approx what percent of students spent more than $400 on materials?
A. 16%
B. 32%
C. 68%
D. 50%
+iClicker
Suppose the amount spent by students on materials for summer half term has approx a normal, bell-shaped distribution. Mean amount spent was $300 and standard deviation was $100.
Approx what percent of students spent more than $400 on materials?
A. 16%
B. 32%
C. 68%
D. 50%
+Example Exam Question
What is P(A)?
What is P(A and B)?
What is P(B|A)
What is P(A and C)?
Are the events A and C mutually exclusive?
+iClicker
How did you feel about the material covered in today’s lab?
A. Completely understood everything
B. Understood main ideas, shaky on details
C. Good for the first half, lost for the second
D. Trouble with some main ideas
E. Difficulty following most material