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:

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:

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)…….. S A B

Rules o’ Probability Continued 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 A&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 T H T H T FLIP 1 FLIP 3 FLIP 2 3H, 0T 2H, 1T 1H, 2T 2H, 1T 1H, 2T 0H, 3T X P(X=0) = 1*P(H C ) 3 =.125 P(X=1) = 3*P(H C ) 2 P(H) =.375 P(X=2) = 3*P(H) 2 P(H C ) =.375 P(X=3) = 1*P(H) 3 =.125

Imagine doing P(5 heads in 9 flips) What we need is a formula… 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 PredictorCoefSTDevT-Ratio P CONSTANT Age S = 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 H 0 when it is actually true Usually not so bad Rejecting a “good” shipment Probability is equal to  Type II – Failing to Reject H 0 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? RedOrangeYellowGreenBlueBrown RedOrangeYellowGreenBlueBrown 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? RedOrangeYellowGreenBlueBrown RedOrangeYellowGreenBlueBrown

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!!!!!!!!!!!