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Notes on Topic 7:
Sample Distributions and Sampling Distributions

    1. Overview

      2. Sample Distributions

      We have seen numerous sample distributions --- distributions of the scores that a variable is observed to have for a sample of individuals.

      Sampling Distributions

      A sampling distribution is a distribution of the values that a specific statistic takes on in all of the possible samples of a specific size from a population. We have not discussed sampling distributions before.

      Example: SAT Math Sample Distribution

      Consider the SAT-Math variable that we observed in the survey done on the first day of class.

      Sample Statistics, Population Parameters
      and Sample Frequency Distribution for SAT Math
      Statistics & Parameters Sample Frequency Distribution
      Sample Statistics
      Samp. Mean = 589.39
      Samp. Stand. Dev. = 94.35


      Legend: Red = males; Blue = females.
      Population Parameters
      Pop. Mean = 460
      Pop. Stand. Dev. = 100

      What Inferences can we make?

      We might wonder what the

    2. Introduction to Statistical Inference

      3. Definition
      Probability is defined for a specific outcome in a situation where several different outcomes are possible. If the possible outcomes are denoted A, B, C, D, etc., then the probability of A is defined as: