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Performing Hypothesis Tests: Means definitions

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  • Null Hypothesis
    Default assumption about a population parameter, typically stating no effect or no difference.
  • Alternative Hypothesis
    Statement suggesting a different claim about a population parameter, often what the test seeks evidence for.
  • Population Mean
    Average value of a characteristic for all members of a group under study, denoted by the Greek letter mu.
  • Population Standard Deviation
    Measure of spread for all values in a population, represented 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 for values in a sample, represented by the letter s.
  • Significance Level
    Threshold probability, denoted by alpha, used to decide whether to reject the null hypothesis.
  • Test Statistic
    Calculated value summarizing sample data, used to determine how far the sample result is from the hypothesized value.
  • Z-Test
    Statistical test used when the population standard deviation is known and the sample size is sufficiently large.
  • T-Test
    Statistical test used when the population standard deviation is unknown, relying on the t-distribution.
  • P-Value
    Probability of observing a test statistic as extreme as, or more extreme than, the one calculated, assuming the null hypothesis is true.
  • Degrees of Freedom
    Value calculated as sample size minus one, used in t-distribution calculations.
  • Random Sample
    Subset of a population selected so that every member has an equal chance of being chosen.
  • Normal Distribution
    Symmetrical, bell-shaped curve describing the spread of a characteristic in a population.
  • Critical Value
    Cutoff point on the test statistic distribution used to decide whether to reject the null hypothesis.