Transcript AP Stat Essential Stuff - Woodside Priory School

AP Stat Essential Stuff
Final Review Before AP Exam
May 2007
Boxplots and Calculating
Outliers
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8, 10, 18, 18, 19, 19, 19, 24, 32, 45
Median:
Q1:
Q3:
Outliers?
Commenting on Distributions:
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2.
3.
4.
Linear Regression
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Draw an LSRL. Now add a data point
that would have a positive residual.
Show how it is calculated.
If r=.6932 explain what this means,
what if r=.4522, r= -.89, r=.02
Explain an r-squared of 0.88 if the
variables were age (x) and weight (y)
Commenting on Scatterplots:
1.
2.
3.
4.
5.
Cumulative Frequency Plot
Binomial vs. Geometric
PDF vs CDF
Examples
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I shoot 10 free throws, If I am a 80% FT
shooter, what is probability that I make
exactly 7 or 8?
How many shots, on average, before I
miss?
What is probability my first miss is on or
before my 4th shot?
Rules o’ Probability
If two events are disjoint (mutually exclusive),
they have no outcomes in common. For
example, in craps, rolling a 5 AND a 7 is disjoint,
one roll can’t produce both outcomes.
Therefore (for disjoint events):
P( AorB)  P( A)  P( B)
AND (for disjoint events)……..
P( AandB)  0
S
A
B
Rules o’ Probability Continued
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If two events are NOT disjoint (not mutually exclusive)
but ARE independent . For example, roll 2 dice
Event A: Die 1 Shows a 6 P(A)=1/6
Event B: Die 2 Shows a 6 P(B)=1/6
P(A and B)= P(A)*P(B)
= 1/6 * 1/6 = 1/36 = .028ish
S
A
B
Disjoint Events Are NOT
Independent
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Hurting your brain?
Just think…If I roll two die and add up
the pips, what are the chances that I get
a 5 and a 7.
S
That’s why (in disjoint
Roll 5
events)
Roll 7
P(A and B)=0
Conditional Probability
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I will flip a coin. If it lands heads I will
study for 4 hours tonight. If it is tails, I
will hang out with Gamburd and talk
about Grey’s Anatomy.
If I study for 4 hours I have a 90%
chance of passing. If not, I have only a
50% chance of passing.
Conditional Probability 2
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If I go ahead with my plan, what is the
probability that I fail the test?
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Given that I passed the test, what is the
probability that I had studied for 4
hours?
Binomial Probability
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If 3 coins flipped, X = # of Heads
H 3H, 0T
H
T 2H, 1T
H
H 2H, 1T
T
H
T
FLIP
1
T
FLIP
2
0
1
2
3
1
3
3
1
T 1H, 2T
H 2H, 1T
P(X=0) = 1*P(HC)3 = .125
T 1H, 2T
H 1H, 2T
P(X=2) = 3*P(H)2 P(HC) = .375
T 0H, 3T
FLIP
3
X
P(X=1) = 3*P(HC)2 P(H) = .375
P(X=3) = 1*P(H)3 = .125
Imagine doing P(5 heads in 9
flips)
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What we need is a
formula…
Insert binomial
coefficient here…
n k
n k
P( X  k )    p (1  p)
k 
Matched Pairs / Blocking
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Blocks or pairs should be similar with
respect to what is being blocked for.
Example, block for age and gender if
there are two treatments.
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22M, 25F, 34M, 40M, 28M, 49F, 32F, 44F
How to assign treatments? “Describe a
method”
Simulation
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Scheme
Stopping Rule
Count
Non-Replacement
T versus Z Procedures
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Use T When:
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Use Z When:
Confidence Intervals
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Find Formula on Formula Sheet
Estimate +/- (Critical Value)(SD of statistic)
CI Stuff
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Interpreting 99% CI (12.34, 15.56) Mean age of first Kiss…
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Interpreting CL of 99%
MOE Problem
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We want a 95% CI for the percent of
Priory students who prefer volleyball
over basketball. It is assumed that 60%
prefer Vball over Bball. What sample
size will we need if the MOE is to be no
more than 5%
Reading Computer Output
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Predictor
Coef
STDev T-Ratio
P
CONSTANT
44.01
1.827
24.09
.000
Age
0.993
0.065
15.23
.000
S = 1.538
R-sq = 95.9%
R-sq(adj) = 95.5%
Find LSRL if this data is showing age (x) and
average wage per hour in Nuevo Sols (y)
Construct a 95% CI if n=40
Power and Error Wrap
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What you have to know:
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Explain Power, Type I, and Type II errors in
context of the problem.
Calculate P(Type I error) given 
How to Decrease:
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Type I Error
Type II Error
How to increase Power
Errors
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Type I – Reject H0 when it is actually true
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Usually not so bad
Rejecting a “good” shipment
Probability is equal to 
Type II – Failing to Reject H0 when it is actually
false
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Usually bad
Accepting a “bad” shipment
Probability () is a bear to calculate
Errors - #2
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Decrease both Type I and II errors by:
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Increasing n
Decrease Type II Errors by:
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Increasing 
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You end up rejecting more/failing to reject less
Causes an increase in Type I errors
POWER
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Basically, how sure we are that we will not
get a Type II error
Power = 1 – P(Type II)
OR Power = 1 - P()
Never will you be asked to compute (unless
the probability of a type II error is given)
Increase Power by:
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Increasing n (Sample size)
Increase  (say from .01 to .05)
Interpreting P-Value In
Context
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Say my null was:
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My Alt Was:
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No difference between proportion of boys
and girls in regards to handwashing after
potty use
There is a difference…
What if p=0.003, 0.599, 2.877?
Chi-Square Love
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Goodness of Fit
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Independence
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Homogeneity
Which one? Do It…
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I open 20 packs of M&M’s and get this:
Red
Orange
Yellow
Green
Blue
Brown
120
159
153
184
229
155
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The Company says I should get the
following proportions:
Red
Orange
Yellow
Green
Blue
Brown
13%
14%
13%
20%
24%
16%
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Is there any evidence that they are not
being truthful in their claim?
Which one? Do It…
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I open 20 packs of Plain M&M’s and get this:
Red
Orange
Yellow
Green
Blue
Brown
120
159
153
184
229
155
My Friend opens 20 packs of peanut M&M’s
and gets this:
Red
Orange
Yellow
Green
Blue
Brown
142
148
164
155
245
139
Is there any evidence of a difference in the
distribution of colors between plain and
peanut M&M’s?
Key Words To Look For:
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Chi Square Independence:
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Association, dependent, independent, link
Chi Square Homogeneity:
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Difference, consistent, proportions, same,
similar, distribution
Overall Tips
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Relax and read the question. Look for
tips
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Example …..relationship between….
improvement…difference…
Keep scoring in mind
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Guessing Penalty
On FR, do #1 or #2, then try #6, read other
questions and do in order of confidence
More tips
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Answer questions in context. Communication is key.
Follow directions, look for words like explain, justify or
describe.
No “BullSnooting”, you are graded on everything you
write, so if part of your answer is wrong, you will be
marked down.
Amount of space on a FR problem is not necessarily
indicative of the amount of work you must show.
If you can’t find an answer to one part, make
something reasonable up and continue on to the next
part of the problem
What to do now…
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Re-read the unit review notes
Focus on things you have had trouble
with.
Check that you have:
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Your calc with batteries
Pencils
Sleep well the night before
Kick some booty!!!!!!!!!!!