AP Stat Essential Stuff

Final Review Before AP Exam

May 2007

Boxplots and Calculating Outliers 8, 10, 18, 18, 19, 19, 19, 24, 32, 45 Median: Q1: Q3: Outliers?

Commenting on Distributions:

1.

2.

3.

4.

Linear Regression 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 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):

AND (for disjoint events)……..

( ) ( ) ( )P AorB P A P B= +

( ) 0P AandB =

S

A

B

Rules o’ Probability Continued If two events are NOT disjoint (not mutually exclusive)

but ARE independent . For example, roll 2 diceEvent 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

BA&B

Disjoint Events Are NOT Independent 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.

That’s why (in disjoint

events)

P(A and B)=0

S

Roll 5

Roll 7

Conditional Probability 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 If I go ahead with my plan, what is the

probability that I fail the test?

Given that I passed the test, what is the probability that I had studied for 4 hours?

Binomial Probability If 3 coins flipped, X = # of Heads

H

T

H

T

H

T

H

T

H

TH

TH

TFLIP 1

FLIP 3

FLIP 2

3H, 0T

2H, 1T

2H, 1T

1H, 2T

2H, 1T

1H, 2T1H, 2T

0H, 3T

X 0 1 2 3

1 3 3 1

P(X=0) = 1*P(HC)3 = .125

P(X=1) = 3*P(HC)2 P(H) = .375

P(X=2) = 3*P(H)2 P(HC) = .375

P(X=3) = 1*P(H)3 = .125

Imagine doing P(5 heads in 9 flips)

What we need is a formula…

( ) (1 )k n knP X k p p

k−⎛ ⎞

= = −⎜ ⎟⎝ ⎠

Insert binomial coefficient here…

Matched Pairs / Blocking 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. 22M, 25F, 34M, 40M, 28M, 49F, 32F, 44F

How to assign treatments? “Describe a method”

Simulation Scheme Stopping Rule Count Non-Replacement

T versus Z Procedures Use T When:

Use Z When:

Confidence Intervals Find Formula on Formula Sheet

Estimate +/- (Critical Value)(SD of statistic)

CI Stuff Interpreting 99% CI (12.34, 15.56) -

Mean age of first Kiss…

Interpreting CL of 99%

MOE Problem 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

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

PredictorCoef 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%

Power and Error Wrap What you have to know:

Explain Power, Type I, and Type II errors in context of the problem.

Calculate P(Type I error) given How to Decrease:

Type I Error Type II Error

How to increase Power

Errors

Type I – Reject H0 when it is actually true Usually not so bad Rejecting a “good” shipment Probability is equal to

Type II – Failing to Reject H0 when it is actually false Usually bad Accepting a “bad” shipment Probability () is a bear to calculate

Errors - #2 Decrease both Type I and II errors by:

Increasing n Decrease Type II Errors by:

Increasing You end up rejecting more/failing to reject less Causes an increase in Type I errors

POWER 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:

Increasing n (Sample size) Increase (say from .01 to .05)

Interpreting P-Value In Context Say my null was:

No difference between proportion of boys and girls in regards to handwashing after potty use

My Alt Was: There is a difference…

What if p=0.003, 0.599, 2.877?

Chi-Square Love Goodness of Fit

Independence

Homogeneity

Which one? Do It… I open 20 packs of M&M’s and get this:

The Company says I should get the following proportions:

Is there any evidence that they are not being truthful in their claim?

Red Orange Yellow Green Blue Brown

120 159 153 184 229 155

Red Orange Yellow Green Blue Brown

13% 14% 13% 20% 24% 16%

Which one? Do It… I open 20 packs of Plain M&M’s and get this:

My Friend opens 20 packs of peanut M&M’s and gets this:

Is there any evidence of a difference in the distribution of colors between plain and peanut M&M’s?

Red Orange Yellow Green Blue Brown

120 159 153 184 229 155

Red Orange Yellow Green Blue Brown

142 148 164 155 245 139

Key Words To Look For: Chi Square Independence:

Association, dependent, independent, link Chi Square Homogeneity:

Difference, consistent, proportions, same, similar, distribution

Overall Tips Relax and read the question. Look for

tips Example …..relationship between….

improvement…difference… Keep scoring in mind

Guessing Penalty On FR, do #1 or #2, then try #6, read other

questions and do in order of confidence

More tips 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… Re-read the unit review notes Focus on things you have had trouble

with. Check that you have:

Your calc with batteries Pencils

Sleep well the night before Kick some booty!!!!!!!!!!!