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AP Stat Essential Stuff

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.

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AP Stat Essential Stuff

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  1. AP Stat Essential Stuff Final Review Before AP Exam May 2007

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

  3. Commenting on Distributions:

  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)

  5. Commenting on Scatterplots:

  6. Cumulative Frequency Plot

  7. Binomial vs. Geometric

  8. PDF vs CDF

  9. 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?

  10. 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

  11. 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 A&B B

  12. 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

  13. 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.

  14. 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?

  15. 3H, 0T H H 2H, 1T T H H 2H, 1T T T 1H, 2T H 2H, 1T H T 1H, 2T T H 1H, 2T T FLIP 1 T 0H, 3T FLIP 2 FLIP 3 Binomial Probability • If 3 coins flipped, X = # of Heads 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

  16. Imagine doing P(5 heads in 9 flips) • What we need is a formula… Insert binomial coefficient here…

  17. 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”

  18. Simulation • Scheme • Stopping Rule • Count • Non-Replacement

  19. T versus Z Procedures • Use T When: • Use Z When:

  20. Confidence Intervals • Find Formula on Formula Sheet Estimate +/- (Critical Value)(SD of statistic)

  21. CI Stuff • Interpreting 99% CI (12.34, 15.56) - Mean age of first Kiss… • Interpreting CL of 99%

  22. 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%

  23. Reading Computer Output 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

  24. 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

  25. 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

  26. 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

  27. 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)

  28. 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?

  29. Chi-Square Love • Goodness of Fit • Independence • Homogeneity

  30. 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?

  31. 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?

  32. Key Words To Look For: • Chi Square Independence: • Association, dependent, independent, link • Chi Square Homogeneity: • Difference, consistent, proportions, same, similar, distribution

  33. 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

  34. 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

  35. 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!!!!!!!!!!!

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