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Performing Hypothesis Tests: Means definitions

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  • Null Hypothesis
    Default assumption about a population parameter, typically stating equality with a specific value.
  • Alternative Hypothesis
    Contrasting claim to the default, often suggesting a difference or inequality in the population parameter.
  • Population Mean
    Average value for all members of a group, represented by the Greek letter mu.
  • Population Standard Deviation
    Measure of spread for all values in a population, denoted by the Greek letter sigma.
  • Sample Mean
    Average value calculated from a subset of the population, often denoted as x bar.
  • Sample Standard Deviation
    Measure of spread within a sample, represented by the letter s.
  • Z-Test
    Statistical test used when the population standard deviation is known, based on the normal distribution.
  • T-Test
    Statistical test applied when the population standard deviation is unknown, relying on the t distribution.
  • Test Statistic
    Numerical value summarizing sample data for comparison against a theoretical distribution.
  • P-Value
    Probability of observing a result as extreme as the sample, assuming the null hypothesis is true.
  • Significance Level
    Threshold probability, denoted by alpha, used to decide whether to reject the null hypothesis.
  • Degrees of Freedom
    Value calculated as sample size minus one, crucial for determining the shape of the t distribution.
  • Normal Distribution
    Bell-shaped curve describing the spread of values in many populations, used in z-tests.
  • Random Sample
    Subset of a population selected so each member has an equal chance of inclusion.
  • Left-Tailed Test
    Hypothesis test where the alternative hypothesis claims the parameter is less than a specified value.