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Critical Values and Rejection Regions definitions

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  • Critical Value
    A threshold from the alpha level that separates expected test statistics from those considered statistically unusual.
  • Rejection Region
    The area beyond the critical value(s) where test statistics provide strong evidence against the null hypothesis.
  • Alpha Level
    The probability threshold, often 0.05 or 0.01, used to determine the size of the rejection region in hypothesis testing.
  • Test Statistic
    A calculated value, such as z or t, that summarizes sample data for comparison against a critical value.
  • Null Hypothesis
    A default assumption about a population parameter, typically stating no effect or no difference.
  • Alternative Hypothesis
    A statement indicating the presence of an effect or difference, opposing the null hypothesis.
  • Left-Tailed Test
    A hypothesis test where the rejection region is in the lower tail of the distribution, indicating values less than expected.
  • Right-Tailed Test
    A hypothesis test where the rejection region is in the upper tail, indicating values greater than expected.
  • Two-Tailed Test
    A hypothesis test with rejection regions in both tails, used when deviations in either direction are significant.
  • Z Table
    A reference chart providing probabilities or critical values for the standard normal distribution.
  • P Value
    The probability of observing a test statistic as extreme as, or more extreme than, the one calculated, assuming the null hypothesis is true.
  • Sample Size
    The number of observations or data points included in a statistical sample.
  • Population Standard Deviation
    A measure of variability in the entire population, often denoted by sigma (σ), used in test statistic calculations.
  • Test Criteria
    The conditions that must be met for the results of a hypothesis test to be valid, such as normality or sufficient sample size.
  • Significance Level
    Another term for alpha level, representing the probability of making a Type I error in hypothesis testing.