AP Statistics Final Exam Review!!!!!

Experimental Design Random Sampling Stratified Sampling Convenience Sampling Cluster Sampling Systematic Sampling Multistage Sampling Census etc…………

Percentiles Ex: A random sample of size 25 is taken from a normal population having a mean 200 and standard deviation 10. What is the 95th percentile?

Probability!! Formulas: P(A and B)=P(A)P(B) If they are independent P(A or B)=P(A) + P(B) If they are mutually exclusive OR P(A or B)=P(A) + P(B)- P(A and B) if they have two events in common!! P(AІB)= P(A and B)/ P(B)

Probability Examples Ex 1: The probability I like Pretzels is .45. The probability I likes Bagels is .25. The probability I like Pretzels and Bagels is .35. Are these 2 events independent? Is P(P and B)=P(P)*P(B)? 0.35 ≠ (0.45)(0.25) Therefore they are not independent!

Ex 2: The probability that I play volleyball on Tuesday is 0. 9 Ex 2: The probability that I play volleyball on Tuesday is 0.9. The probability that I play volleyball and go running on Tuesday is 0.6. What is the probability I went running, given that I went to volleyball? P(R|V)= 0.6/0.9=0.6667

Error in a Significance Test Type I: (α) -Reject H₀ when in fact H₀ is true. Type II: (β) -Accept H₀, when in fact H₀ is true. ** Remember to define and also state in terms of the problem

Confidence Intervals http://www.stat.tamu.edu/~west/applets/ci.html

Density Curves The area under any density curve= 1 Ex: Does the following function represent a density curve?

She scored better on the SAT Z-scores Jen scored a 1240 on her SAT and a 27 on her ACT. The SAT has a mean of 1080 and a std. dev. of 100 while the ACT has a mean of 25 with a std. dev. of 2.3. Which test results should she report on her college applications? SAT = (1240-1080)/100=1.6 ACT= (27-25)/2.3=0.87 She scored better on the SAT

Characteristics of a t-curve With your partners, think of 2 characteristics that apply to a t-distribution Asymptotic w/ the x-axis and extends infinitely to the left and right Hint: How do we define a t-curve? Mean & Standard Deviation?

How measures of center are affected What happens to the: -mean -standard deviation -median -correlation If I double everyone’s quiz grade. If I add 5 extra credit points to everyone’s quiz grade.

What is a “p-value”???? Assuming Ho is true, there is a 2.37% chance of observing a value as extreme or more extreme than the one observed.

Binomial Distribution -There are a fixed # of trials -They are independent -The probability of success, p, is the same -There are 2 outcomes, success or failure.

Binomial Distribution Example The probability I hit a triple is 0.24. What is the probability of getting at least one triple in 6 of my at-bats? Ans: 1-P(no triples)= 1 – P(0)=

Prediction was too high Residuals Residuals: Observed – Predicted R= O-P What does it mean if we get a negative residual? Prediction was too high Positive? Prediction was too low

Probability Distributions? What is the expected value? x 1 2 3 4 P(x) 1/3 1/4 1/6 μ= 1(1/3) + 2(1/4) + 3(1/4) + 4(1/6) = 2.25

Central Limit Theorem What is the difference between the central limit theorem and the law of large numbers?

Margin of Error One sample t-interval One proportion z-interval

Free Response Questions There will be 4 free response questions. They could include any of the following topics. -Probability- Are they independent? -Experimental Design -Binomial Distribution -Significance Tests: Matched pairs t-test 2 Sample t-test Chi-Squared Test Linear Regression Test