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Experimental Design and Hypothesis Testing
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Experimental Design and Hypothesis Testing

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Questions and Answers

What is the main characteristic of a designed experiment?

  • It looks back at past data to identify relationships between variables.
  • It asks a lot of people a few well-constructed questions.
  • It actively manipulates variables to observe their effect on a specific outcome. (correct)
  • It observes real-world conditions without manipulating variables.
  • What is the purpose of a two-sample hypothesis test?

  • To ask a lot of people a few well-constructed questions.
  • To compare two population parameters using data from two independent samples. (correct)
  • To test a hypothesis about a single population parameter.
  • To identify relationships between variables in past data.
  • What is an axiom in the context of statistics?

  • A method of data collection.
  • A statement that is taken to be true, to serve as a premise. (correct)
  • A type of probability distribution.
  • A hypothesis to be tested.
  • What describes the relative likelihood of a random variable taking on different possible values?

    <p>Probability Distribution.</p> Signup and view all the answers

    What is the advantage of the Cumulative Distribution Function (CDF)?

    <p>It can be defined for any kind of random variable, whether discrete, continuous, or mixed.</p> Signup and view all the answers

    What is a fractional factorial experiment design?

    <p>A variation of the basic factorial arrangement in which only a subset of the factor combinations are actually tested.</p> Signup and view all the answers

    What is the purpose of an observational study?

    <p>To observe real-world conditions for a period of time without manipulating variables.</p> Signup and view all the answers

    What is the purpose of a survey?

    <p>To ask a lot of people a few well-constructed questions.</p> Signup and view all the answers

    Study Notes

    Experiment Designs

    • Designed experiment: actively manipulates variables to observe their effect on a specific outcome
    • Factorial experiment design: uses every possible combination of factor levels to form a basic experiment with "k" different settings for the process
    • Fractional factorial experiment design: a variation of the basic factorial arrangement, testing only a subset of the factor combinations

    Hypothesis Testing

    • One-sample hypothesis: tests a hypothesis about a single population parameter based on data from a single sample
    • Two-sample hypothesis: compares two population parameters using data from two independent samples

    Study Types

    • Observational study: observes real-world conditions for a period of time without manipulating variables
    • Retrospective study: looks back at past data to identify relationships between variables
    • Survey: a method to ask a lot of people a few well-constructed questions, with a series of unbiased questions that the subject must answer

    Probability and Statistics

    • Axiom: a postulate, assumption, or a statement that is taken to be true, serving as a premise for further reasoning and arguments
    • Probability distribution: describes the relative likelihood of a random variable taking on different possible values
    • Probability mass function: used for discrete random variables
    • Probability density function: used for continuous random variables
    • Cumulative Distribution Function (CDF): describes the distribution of random variables, can be defined for any kind of random variable (discrete, continuous, or mixed)
    • Expected value (mean): provides a measure of the central tendency of a probability distribution, calculated using the equation E(X) = ...
    • Variance: measures the degree of spread or dispersion of the values of a variable around the expected value (mean), calculated using the formula V(X) = ...
    • Standard deviation: the square root of the variance, providing a measure of the amount of variation or dispersion in a set of values

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    Description

    Test your knowledge of experimental design, including factorial and fractional factorial designs, and hypothesis testing for a single population parameter.

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