10 & 11 - Random Sampling and Sampling Distributions

10 & 11 - Random Sampling and Sampling...

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Chapters 10 & 11: Probability, Random Sampling and Sampling Distributions
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Begin our discussion of inferential statistics Make inferences about population parameter on the basis of a sample statistic Understanding how we do this means understanding a few things about how we calculate probability
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Theorems of Probability Sections 10.1-10.3 in book We use an Equally-Likely Model of Probability All possible outcomes are equally likely to occur E.g: When rolling a six-sided die, each number is equally likely to occur (Pr = 1/6)
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Addition Theorem of Probability Add probabilities when predicting likelihood of any one of several particular events E.g., if I roll a die once, what is the probability it will land on 1 or 3 or 5? Pr (1) = 1/6 Pr (3) = 1/6 Pr (5) = 1/6 1/6 + 1/6 + 1/6 = 3/6 or 1/2 Also known as the “or” rule
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Only works when events are mutually exclusive Occurrence of one outcome precludes the possibility of all other outcomes.
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Multiplication Theorem Of Probability Multiply probabilities when predicting successive or joint events E.g., If I roll my die twice, what is the probability I will get a 3 on the first roll and a 5 on the second roll? 1/6 x 1/6 = 1/36 Also known as the “and” rule
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When multiplying probabilities, important that the events are independent Outcome of one event does not influence the outcome of other events
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These theorems can be used in combination: E.g, If I roll two dice at once, what’s the probability or rolling a 5 and a 6?
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