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AP Statistics Semester One Review Part 2 Chapters 4-6 AP Statistics Topics Describing Data Producing Data Probability Statistical Inference Chapter 4: Designing Studies In this chapter, we learned methods for collecting data through sampling and experimental design. Sampling Design Our goal in statistics is often to answer a question about a population using information from a sample. to do this, the sample must be representative of the population in question Observational Study vs. Experiment If you are performing an observational study, Sampling your sample can be obtained in a number of ways: Convenience Sample Simple Random Sample Stratified Random Sample Systematic Random Sample Experimental Design In an experiment, we impose a treatment with the hopes of establishing a causal relationship. 3 Principles of Experimental Design Randomization Control Replication Experimental Designs Experiments can take a number of different forms: Completely Randomized Design Randomized Block Design Matched Pairs Design Chapter 5: Probability: What are the Chances? This chapter introduced us to the basic ideas behind probability and the study of randomness. We learned how to calculate and interpret the probability of events in a number of different situations. Probability Probability is a measurement of the likelihood of an event. It represents the proportion of times we’d expect to see an outcome in a long series of repetitions. Probability Rules The following facts/formulas are helpful in calculating and interpreting the probability of an 0event: ≤ P(A) ≤ 1 P(SampleSpace) = 1 P(AC) = 1 - P(A) P(A or B) = P(A) + P(B) - P(A and B) P(A and B) = P(A) P(B|A) A and B are independent if and only if P(B) = P(B|A) Strategies When calculating probabilities, it helps to consider the Sample Space. List all outcomes, if possible Draw a tree diagram or Venn diagram Sometimes it is easier to use common sense rather than memorizing formulas! Chapter 6: Random Variables This chapter introduced us to the concept of a random variable. We learned how to describe an expected value and variability of both discrete and continuous random variables. Random Variable A Random Variable, X, is a variable whose outcome is unpredictable in the short-term, but shows a predictable pattern in the long run. Discrete vs. Continuous Expected Value The Expected Value, E(X) = µ, is the long-term average value of a Random Variable E(X) for a Discrete X Variance 2 σ, The Variance, Var(X) = is the amount of variability from µ that we expect to see in X. The Standard Deviation of X, Var(X) for a Discrete X Rules for Means and Variances The following rules are helpful when working with Random Variables. Linear Transformations on Random Variables Sums & Differences of Random Variables Some Random Setting Variables are the result of Binomial events that have only two outcomes (success and failure). We define a Binomial Setting to have the following features: Binary Situations (Two Outcomes success/failure) Independent trials Number of trials is fixed - n Probability of success is equal for each trial IfBinomial X is B(n,p), the following formulas can be Probabilities used to calculate the probabilities of events in X. The mean and standard deviation of a binomial distribution simplifies to the following formulas: Some Random Variables are the result of Geometric Setting events that have only two outcomes (success and failure), but have no fixed number of trials. We define a Geometric Setting to have the following features: Binary Situations (Two Outcomes success/failure) Independent trials Trials continue until a success occurs Probability of success is equal for each trial Geometric Probabilities If X is Geometric, the following formulas can be used to calculate the probabilities of events in X. The mean of a geometric distribution simplifies to the following formula: Semester One Final Exam 50 Questions Multiple Choice Chapters 1-6 Tuesday and Wednesday