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Performing Hypothesis Tests: Variance definitions

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  • Population Variance
    Represents the spread of values in an entire population, often denoted as sigma squared.
  • Sample Variance
    Measures the variability within a sample, calculated as the average squared deviation from the sample mean.
  • Chi-Square Test Statistic
    A value computed to assess claims about variance, using the formula n-1 times sample variance divided by expected variance.
  • Degrees of Freedom
    Indicates the number of independent values in a calculation, found by subtracting one from the sample size.
  • Null Hypothesis
    A statement asserting that the population variance equals a specified value, serving as the default assumption.
  • Alternative Hypothesis
    A claim suggesting the population variance differs from the specified value, often greater or less than.
  • Significance Level
    A threshold, denoted as alpha, used to decide whether to reject the null hypothesis based on the p-value.
  • P-Value
    The probability of observing a test statistic as extreme as the one calculated, assuming the null hypothesis is true.
  • Random Sample
    A subset of data selected so each member of the population has an equal chance of inclusion.
  • Normal Distribution
    A symmetric, bell-shaped distribution required for valid variance hypothesis testing.
  • Right Tail Probability
    The likelihood that the test statistic exceeds a certain value, relevant for greater-than alternative hypotheses.
  • Test Statistic
    A calculated value used to compare observed data with what is expected under the null hypothesis.
  • Hypothesis Test
    A procedure for evaluating claims about population parameters using sample data and statistical methods.
  • Sigma Squared
    The notation for population variance, representing the average squared deviation from the mean.
  • Alpha
    The chosen probability threshold for making decisions in hypothesis testing, commonly set at 0.05 or 0.1.