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Performing Hypothesis Tests: Variance definitions

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  • Population Variance
    A measure of how data points in an entire group differ from the group mean, often denoted as sigma squared.
  • Sample Variance
    A calculation showing how much sample data values deviate from their mean, used as an estimate for population variance.
  • Chi-Square Statistic
    A value computed to compare observed sample variance to expected population variance in hypothesis testing.
  • Null Hypothesis
    A statement asserting that the population variance equals a specific value, serving as the default assumption.
  • Alternative Hypothesis
    A claim suggesting the population variance differs from the hypothesized value, representing what evidence is sought for.
  • Alpha Level
    A threshold probability, often set before testing, used to decide whether to reject the null hypothesis.
  • Degrees of Freedom
    A value, typically sample size minus one, needed to determine the correct chi-square distribution for the test.
  • P-Value
    A probability indicating how likely the observed test statistic would occur if the null hypothesis were true.
  • Right Tail Probability
    The likelihood that the test statistic is greater than a certain value, used in one-sided variance tests.
  • Random Sample
    A subset of data chosen so every member of the population has an equal chance of selection, ensuring unbiased results.
  • Normal Distribution
    A bell-shaped data pattern required for valid variance hypothesis testing, ensuring accurate probability calculations.
  • Test Statistic
    A calculated value summarizing sample data for comparison against a theoretical distribution in hypothesis testing.
  • Quality Control
    A process in manufacturing or service settings where statistical tests are used to monitor and maintain product consistency.
  • Statistical Inference
    The process of drawing conclusions about a population's characteristics based on sample data analysis.
  • Sigma Squared
    A symbol representing the variance of a population, central to hypothesis tests about variability.